Somehow, someway a transformation has to be generated to affect the planets surface temperature.
You cant just say RADIATIVE energy get converted into HEAT. Its more likely it stays RADIATIVE energy. There has to be a PROCESS.
What the current scientific view does is to confuse solar flux's W/m² with heat's cal.
W/m² is NOT cal/m²...
When we say for Planet Radiative Energy Budget
energy in = energy out
then what we refer to is the radiative energy. Radiative energy is measured in W/m² unit.
W/m² is radiative energy intensity measure, it is not an amount of heat added to planetary surface, as one might think.
The not reflected portion of the incident on the planet surface radiative energy does not get ENTIRELY absorbed AS HEAT .
What radiative energy does is to INTERACT with the surface's matter. The planet average surface specific heat "cp" and the planet rotational spin "N" are of the major factors in the "radiative energy  planet surface" INTERACTION PROCESS.
In planetary surface Radiative Equilibrium the entire incident solar radiative energy is reradiated out.
1). On the spot and on the very instant the partial SW Reflection (specular and diffuse) of the incident radiative flux.
2). On the spot and on the very instant IR emission of a transformed from SW into LW fraction of the not reflected portion.
3). On the very instant and on the spot the rest of the not reflected and not IR emitted solar radiative energy gets accumulated in form of heat in the surface's inner layers.
The amount of heat accumulated in the surface's inner layers will later (at the night time hours), it will also be IR emitted as outgoing energy.
The amount of heat accumulated in the surface's inner layers is what varies for planet's variations of "the planet average surface specific heatcpand the planet rotational spinN" products.
When INTERACTING with planetary surface the energy is reflected, IR emitted and accumulated at the same time. Only a fraction of EM energy is accumulated in form of HEAT for the later IR emission.
When at nighttime hours surface does not interact with solar flux. At nighttime hours surface emits IR EM radiative energy as the StefanBoltzmann emission law requires.
Surface's spots emit at nighttime hours as previously warmed blackbody spots which they are then.
Conclusion:
There is not any violation of The first law of thermodynamics,when a faster rotating planet appears to be on average a warmer planet.
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Short Summary: What the Research was needed for?
Well, it is a good question. An opponent at one of the first presentations of the New Theory asked:
"Why it should be again explained, what is already explained?"
Well, it was very much obvious to me that the Trace Greenhouse Gases Content in thin Earth's atmosphere were not able to produce any Greenhouse Warming Effect on the Earth's surface.
It was obvious to me... but when discussing the theme with a scientist, who is a specialist in climatology... he was very much certain that without Earth's atmosphere greenhouse effect Earth would have been a snowball.
Science can only progress if assumptions are tested.
The research concluded in deriving a Universal Equation for calculating surface temperatures of planets or moons, for comparison with NASA satellite measurements of such bodies in our solar system.
We had the New theory to explain better…
There is a method we use, which is the comparison method.
In case of the planets surface temperatures it is the“Planets Temperatures Comparison Method”.
The Method lead to discovery of the“Planet Surface Rotational Warming Phenomenon”.
It states that planet mean surface temperatures relate (everything else equals) as their(N*cp) products sixteenth root.
And it is demonstrated in this site, by doing the on various planets the satellite measured mean surface temperatures comparisons, which proved the rightness of the Phenomenon statement.
...........................................
Everything started from two initial notions.
The first notion was the insight that a planet is warmer if the solar lit hemisphere is cooler.
When solar irradiated surface is cooler, the surface IR EM energy emission is weaker (it happens in accordance with the StefanBoltzmann emission law).
So when for the planet Earth the Perihelion coincides around the Winter Solstices Earth is tilted towards sun with its vast Southern Ocean open waters...
In this case (as it happens currently) the closer to the sun waters do not get warmed at much high temperatures during the solar lit hours.
Thus the waters are capable to emit less IR EM radiative energy during the daytime hours. So more energy gets accumulated in the Earth's system.
This is how a New Theory which explains the current Global Warming by the orbital caused forcing emerged.
When we searched for some publications on the planet surface warming cycles we learned about Milankovitch cycle explaining GlacialInterglacial cycles by the orbital forcing.
According to Milankovitch, though, it is the warm summers in Northern Hemisphere what is responsible for Planet Warming. So according to the Milankovitch cycle, Earth should be currently moving thru a Natural Cooling Trend...
So we have accepted the Milankovitch Cycle calculations and graphs, but we have reversed the Milankovitch insight.
 It is the Reversed Milankovitch Cycle we call this unique development of the initial Milankovitch orbital forced GlacialInterglacial cycles.
Yes, everything happens according to the Milankovitch calculations, only the graphs should be read reversed.
When read reversed, the Milankovitch calculations state for the current Global Warming Trend.
There were some happy days, when we thought we have explained the Global Warming Phenomenon...
*******
What we discovered next, was that the initial Milankovitch cycle had been accepted by the Climate Change alarmists as a kind of confirmation of the Human Induced Global Warming.
It is believed that since Earth should be in a Natural cooling trend (according to the Initial Milankovitch cycle) after the Industrial Revolution the Human Induced Global Warming overlapped the Natural cooling trend and the Human influence is so much strong, that instead of the Natural Cooling Trend, Earth has entered in a very dangerous Global Warming Pattern...
It is an obvious fact Earth's atmosphere is very thin... also it is well known the greenhouse gases content in Earth's atmosphere is very small. The greenhouse gases in Earth's atmosphere are trace gases... The greenhouse gases in Earth's atmosphere cannot have any significant supplementary warming effect on Earth's surface, on Earth's climate system.
Nevertheless there is a kind of a dominant Greenhouse Warming theory about the Earth's climate warming. This theory states that greenhouse warming effect on the earth's surface is very strong, it states the greenhouse warming on the earth's surface is veryvery strong, it states it is plus 33oC.
It was obvious the plus 33oC greenhouse enhancement on Earth's mean surface temperature is way too much  Earth's atmosphere is very thin and the greenhouse gases content is a trace gases in a very thin atmosphere... So how it was possible for current science to state that?
In order to understand this scientific paradox we had to study Earth's greenhouse theory from the very basics.
Those basics are two.
First it is the planet surface without atmosphere theoretical blackbody uniform temperature (planet effective temperature Te). For Earth it is Te = 255K.
The second is the Earth's average surface temperature measured as Ts = 288K.
Thus 288K  255K = 33oC (simple, but strange, because it is a comparison between a theoretical uniform Te=255K and a measured average Ts=288K temperatures). We have a comparison of two different physics terms here, this kind of comparison cannot be accepted as an exact science.
A simple thought came up, what about Moon's temperatures then?
Well, for Moon Te = 270K and Ts = 220K (the temperatures are from Wikipedia).
Thus 220K  270K = 50oC (what is this, Moon has not atmosphere, the 50oC for Moon states a kind of a negative greenhouse effect, which is irrational even to suggest).
The next thought was  Earth withoutatmosphere more likely should have a mean surface temperature even lower than Moon's Ts=220K (because Earth has a higher than Moon albedo, thus earth's effective withoutatmosphere temperature instead of Te=255K should be closer to Moon's Ts=220K).
The EarthMoon temperatures comparison was the commence point of the"Planet Temperatures Comparison Method".
We use since the "Planet Temperatures Comparison Method" as a powerful instrument in every step of our research.
The Method is very much valuable because the planets' temperatures are measured physical data, so the "Planet Temperatures Comparison Method" is very much grounded to what actually happens in the real world.
Another reason is that planets' surface temperatures occur in accordance to some basic physics laws. Earth is a planet like any other planet in solar system, and what is right for any other planet should be right for the Earth too.

*******
The second notion was the realization that the solar irradiated smooth surface planets withoutatmosphere reflect solar EM energy not only diffusely, but also specularly.
This second notion led us to the conclusion that a smooth surface planet withoutatmosphere should be considered as analogue to the smooth sphere in the laminar fluid flow.
There is the Drag coefficient for smooth spheres Cd = 0,47
Thus the Φ = 0,47 for smooth surface planets is the solar irradiation accepting factor (planet shape and roughness coefficient).
When we corrected the basic planet uniform blackbody (effective) temperature equation for Earth, by the use in the basic equation of the Φ factor, we obtained for earth's corrected effective temperature the Te.correct = 210K.
So, this second notion, was very successful too.
First it showed that Earth's theoretical Te.correct=210K is indeed lower than Moon's measured mean surface temperature Ts=220K. Thus our thought was confirmed, and, by that, the Φ factor started proving itself as a righteous physics coefficient.
The temperature difference appeared even bigger now.
The difference 288K210K =78oC could not be explained (no matter what) by any of the earth's atmosphere greenhouse effects. (It was something that we knew from the very beginning, it should be a postulate, because it is very much obvious).
That is how our research started  from those two initial notions.
.....................................
The EarthMoon mean surface temperatures paradox is solved.
The Earth's without atmosphere theoretical blackbody temperature Te.earth should be very much close to the Moon's mean surface temperature Tsat.moon
There is the well known scientific paradox  Earth's mean surface temperature Tmean.earth = 288K
Earth's effective temperature is Te.earth = 255K
288K255K = 33oC
Moon's mean surface temperature Tmean.moon = 220K
Moon's effective temperature Te.moon = 270K
220K270K = 50oC
Earth and Moon have some differences, which may explain why the Earth's mean surface temperature is higher by 33oC, and why Moon's mean surface temperature is lower by 50oC.
It is said in the current planetary greenhouse warming approach that the 33oC for Earth is explained by the Earth's atmosphere greenhouse effect
The paradox is that in Moon's case, the current planetary greenhouse warming approach cannot say a word  actually it is very much silent  it is a paradox science has not solved yet.
The planet greenhouse warming effect theory is not capable to explain the why the Moon is on average a much colder planet than Earth.
But there is another difference, which is not taken in account yet. It is the planet surface (N*cp) product.
N  rotations/day is the planet rotational spin
cp  cal/gr.oC is the planet average surface specific heat
The planet (N*cp) product for Earth is "1"
For Moon (N*cp) product is "0,006434"
Moon's (N*cp) product is 1 /0,006434 = 155,4 times smaller than that of Earth.
The planet N*cp product comparison is the development of the first initial notion a planet is warmer if the solar lit hemisphere is cooler.
Also there is the planet corrected effective temperature which is involved. For smooth surface planets and moons withoutatmosphere, or with a thin atmosphere, the Φ(1a) coupled term has Φ=0,47
The Earth's corrected effective temperature Te.correct.earth =210K
The Moon's corrected effective temperature Te.correct.moon =224K
The Φ(1a) coupled term is the development of the second initial notion the realization that the solar irradiated smooth surface planets withoutatmosphere reflect solar EM energy not only diffusely, but also specularly.
When Φ(1a) coupled term was applied instead of the single (1a) a wonderful thing happened. It became possible to precisely estimate the
"energy in"
whch is the left side of the Planet Radiative Energy Balance equation.
And, by having the amount of planet "energy in" correctly estimated it became possible then to successfully formulate the Planet Mean Surface Temperature equation.
This planet mean surface temperature equation obtains planet withoutatmosphere mean surface temperatures very much closely matching the measured by satellites.
And, when seeing it happening, we have one more a very strong argument which very much convincingly proves the absolute rightness of the Φ(1a) coupled term.
Thus, the two initial notions, when developed, have become a scientific method, which is capable to solve the EarthMoon mean surface temperatures paradox.
From now on the Earth and Moon mean surface temperatures are consolidated between them, because now we have the scientific explanation to their so very much different mean surface temperatures.
"Specular reflection from a body of water is calculated by the Fresnel equations.[6] Fresnel reflection is directional and therefore does not contribute significantly to albedo which primarily diffuses reflection."
Our comment:
The planet solar irradiated area from normal point to the terminator of 90o is gradually increasing in dimensions. The further away on the globe's surface from the point of ZENITH INCIDENCE ANGLE to the larger angles of incidence the more extend in dimensions the spherical zones' areas are.
So the larger angles of incidence are accompanied with much larger areas times the much higher the specular reflection portion outgoing to space from them.
Consequently the Φ = 0,47 and the specular reflection of the "waterworld" sphere is expected to be very much comparable.
End of comment.
In order to demonstrate our thought we shall make the effort, and we shall calculate, for the entire solar lit hemisphere, the total amount of the specularly reflected portion of solar flux, based on the above graph's approximate reading data.
We shall divide the by the solar flux lit entire hemisphere in small surface area spherical zones, by proceeding with small 2,5° steps of the angle of incidence variables.
We shall calculate every spherical zone's area (m²) within every and each of this small angle of incidence change 2,5° steps [ θ°(i+1)  θ°i = 2,5° ]
Then we shall read the approximate values on water surface specular reflectivity graph for every chosen for calculation spherical zone (angle of incidence)
(Reflectance of smooth water at 20°C (refractive index 1.333).)
We shall then calculate the product for every small spherical zone area with the related to the same angle of incidence the local reflectance from graph.
Finally we shall summarize all the resulted 2,5° steps (spherical zones * local reflectance from graph) products, and average the sum over the planet's crosssection area, which is perpendicular to solar flux (the area of the perpendicular incidence).
Surface area of spherical zone
A = 2πrh
r  the radius of a planet
h  the height of a spherical zone
The height "h.i " of a spherical zone "i" at the point of solar flux's angular incidence "θ°i"
h.i = [ r*cos θ°i  r*cos θ°(i+1) ] =
= r [ cos θ°i  cos θ°(i+1) ]
Specular reflection from a body of water is calculated by the Fresnel equations.[6] Fresnel reflection is directional and therefore does not contribute significantly to albedo which primarily diffuses reflection.
The radius of a planet is r
The height " h.i " of a spherical zone " i " at the point of solar flux's angular incidence θ°i is
In the above scheme we explain the spherical zone's height calculation method:
h.i = [ r*cos θ°i  r*cos θ°(i+1) ] =
= r [ cos θ°i  cos θ°(i+1) ]
Analysis of terms.
S  the incident on the planet solar flux (W/m²), perpendicular to the planet's crosssection
r  planet's radius (m)
πr²  planet's crosssection area perpendicular to the solar flux's beams (m²)
N  the normal to the surface
θ°  angle of solar flux's incidence
θ°i  angle of solar flux's incidence at i point
h.i = r [ cos θ°i  cos θ°(i+1) ]  the i spherical zone area height
A.i  spherical zone area m² at point i
A.i = 2πr * ( r*cos θ°i  r*cos θ°i+1 )  spherical zone area at i point (m²)
A.i = 2πr² * ( cos θ°i  cos θ°i+1 ) (m²)
...........
Spec.i  ( specular reflectivity at point i ) ( specular reflectivity at point i ) taken from graph for the ( θ°i ) angle of incidence
A.i * Spec.i  the total incident on zone Ai area solar irradiation reflected portion m² *W/m² = W
Σ ( Α.ι* Spec.i )  the Sum total incident on the entire hemisphere's surface solar irradiation reflected portion (W)
Σ ( Α.ι* Spec.i ) /πr²  the total specular reflection portion of the incident solar flux, averaged on the planet's crosssection disk (W/m²)
When substituting terms in the above sentence we would have:
Σ [ 2πr² * ( cos θ°i  cos θ°i+1 ) (m²) * Spec.i W/m² ] /πr² (m²)
When simplifying by eliminating the πr² term
Σ 2 *( cos θ°i  cos θ°i+1 ) * Spec.i (W/m²)  the sphere's total specular reflection portion of the incident solar flux, averaged on the planet's crosssection disk perpendicular to the incoming solar flux
or
2 * Σ [ ( cos θ°i  cos θ°i+1 ) ] * Spec.i (W/m²) (1)
let's symbolize the ( cos θ°i  cos θ°i+1 ) expression with Δcosθ°i term
So we shall write:
2 * Σ Δcosθ°i * Spec.i (W/m²)
Table of data (by 2,5° steps ) and the product ( Δcosθ°i * Spec.i ) results
Angle of
incidence..................cosθ°i  cosθ°i+1 ..graph data.......product
θ°ι...............cos θ°ι.......... Δcosθ°i........Spec.i....... Δcosθ°i * Spec.i
0°......................1.............0,00095..............0....................0
2,5°................0,99905.........0,00285........0,02...............0,00019 5°............0,99619.........0,004750............0,02...............0,000056
7,5°................0,99144.........0,006637......0,02............... 0,000091
10°..........0,98481..........0,0085117............0,02............ 0,000135
12,5°..............0,97630..........0,0104........0,02................ 0,000165 15°..........0,96593............0,01221...........0,02...............0,00020
17,5°..............0,95372...........0,0140...........0,02............. 0,00024
20°..........0,93969............0,0158...........0,02................0,00028
22,5°..............0,92388..........0,0176...........0,02.............. 0,00031 25°..........0,90631............0,0193...............0,02.............0,00035
27,5°..............0,88701...........0,0210........0,02............... 0,00036
30°..........0,86603...........0,0226.............0,02...............0,00042 32,5°..............0,84339...........0,0242..........0,02...............0,000452 35°..........0,81915...........0,0258..............0,02.................0,000484 37,5°.............0,79335...........0,0273.........0,02...............0,000516 40°..........0,76604...........0,0288.............0,02...............0,000546 42,5°.............0,73728............0,0302..........0,023.............0,000662 45°..........0,70711...........0,0315...............0,025...........0,000755 47,5°.............0,67559............0,0329...........0,031............0,00098 50°..........0,64279...........0,0340.................0,035.............0.00115 52,5°..............0,60876...........0,035.............0,037............0,00126 55°..........0,57358..........0,0361.....................0,040.........0,00141 57,5°..............0,53730...........0,0373............0,055............0,00200 . 60°..........0,5....................0,0383...............0,065...........0,00243 62,5°..............0,46175...........0,0391............0,085............0,00325 65°..........0,42262............0,0399.................0,1..............0,003913 67,5°..............0,38268...........0,0407...............0,17...........0,00679 70°..........0,34202.............0,0413................0,22..............0,00895
72,5°..............0,30071..........0,0419...............0,27...........0,01115
75°..........0,25882.......... 0.0424 ...............0,30.............0,01257 77,5°..............0,21644...........0,0428............0,39............0,01653 80°..........0,17365...........0,0431................0,45................0.01926 82,5°..............0,13053...........0,0434.............0,60..............0,02587 85°..........0,08716...........0,0435...............0,70................0,03036 87,5°..............0,04362..........0,0436..............0,82............0,03570 90°...................0...........................................1.............0,04362
Σ....................................................................................0,217
When summarizing from the Table the Δcosθ°i * Spec.i the product results we shall have
Σ Δcosθ°i * Spec.i = 0,217
and multiplying times 2 according to the equation (1) above
2 * Σ Δcosθ°i * Spec.i = 0,217 * 2 = 0,434
 it is the specularly reflected portion of the incident solar flux It is the sphere's total specular reflection portion of the incident solar flux, which is averaged on the planet's crosssection disk.
When considering an oceaniclike planet Earth total reflected energy the diffuse a*So + specular 0,434 *So =
= 0,3 * 1.362W/m² + 0,434 * 1.362W/m² =
= 0,734 * 1.362 W/m² = 999,71 W/m² REFLECTED
and only 1.362  999,71 = 362 W/m² "ABSORBED"
This result (362 W/m² "ABSORBED") is in a satisfactory magnitude accordance with the smooth planet surface the solar incident flux's "absorption" ( 444 W/m² notreflected).
Φ(1  a)So = 0,47(1  0,306)1362 W/m² = 444 W/m² notreflected
when compared with the blackbody theory the 1.362 * (1  0,306) =
= 945 W/m² "ABSORBED"
The difference is more than twice as much!
********
0,434*S specularly reflected from the sea waters...
Now, let's see:
Φ(1 a) *S is the not reflected portion of the incident solar flux.
The sea water Albedo a=0,08
Φ=0,47 for the smooth surface spheres (planets without or with a thin atmosphere)
Φ(1a)*S = 0,47(1  0,08)*S = 0,47*0,92*S = 0,4324*S
it is the not reflected portion of the incident solar flux.