And to address your claim that 'The sky is evaporating'
You wrote:
The other is that the hot molecules or atoms in the upper atmosphere can attain escape velocity and in the process of escaping from the influence of the Earth’s gravitational field can take the extra energy with them.
The root mean square velocity Vrms of a molecule with mass MMolecule in the earths atmosphere at a temperature T is given by:
Vrms= (3kT/MMolecule)1/2.
If T=81F=27C=300K then Vrms for an O2 molecule is 483 m/s. For comparison, the escape velocity is ~11,000 m/s.
Lets increase the temperature, T, to T=37C=310K, then Vrms only grows to 491 m/s...
CLEARLY any realistic heating of the atmosphere will not significantly increase atmospheric loss... THERE, I have done the numbers that you were too lazy or incompetent to do for yourself, will you PLEASE stop dumping your delusions on us?