A Planet Effective Temperature Complete Formula Te = [ Φ (1-a) S (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴

Plus the introduction to the Reversed Milankovitch Cycle. Click on the box for more

The faster a planet rotates (n2>n1) the higher is the planet’s average (mean) temperature T↑mean

The faster a planet rotates (n2>n1) the higher is the planet’s average (mean) temperature T↑mean:

Tmin→ T↑mean ← Tmax

when n2>n1 (it happens because Tmin grows faster than Tmax goes down)

It happens in accordance to the Stefan-Boltzmann Law.

Let's explain:

Assuming a planet rotates faster and Tmax1-Tmax2 = 1 oC.

Then, according to the Stefan-Boltzmann Law:

Tmin2-Tmin1 > 1oC

Consequently  Tmean2 > Tmean1

 

If the solar irradiated hemisphere average temperature

T1-T2=1oC

Then the dark hemisphere average temperature

T2-T1>1oC

Consequently the total average

Tmean2 > Tmean1

So we shall have:

Tmin→ T↑mean ← Tmax

The faster a planet rotates (n2>n1) the higher is the planet’s average (mean) temperature T↑mean.