Maintain atmosphere on moon using global warming

So, a neat thing, depending on how you look at it, about greenhouse gases is that while it's causing a raise in temperature near the surface it actually makes the upper parts of the atmosphere decrease in temperature. Venus is a good example of this.

Now on another note, atmospheric escape depends significantly on the planet/moon's escape velocity and the atmospheric temperature. The lower the temperature then the lower escape velocity a planet can have and still maintain their atmospheres for a significant amount of time. Titan is a good example of this.

What I'm curious about is if a smaller planet, like perhaps our moon, had a larger amount of greenhouse gases than here on Earth which in turn would cause a significantly lower temperature in the upper atmosphere which then would that be enough to slow down gases that are attempting to escape to space, so that the atmosphere would last at least for millions of years. (As of now, the best calculations I have seen so far puts an Earthlike atmosphere on the moon lasting for roughly 700,000 years).

It is my thoughts that the upper atmosphere would work similar to the cold trap we have on Earth, only instead of freezing the gases it instead slows them down enough for the Moon to pull them back in.

Any opinions on this or calculations for this?

P.s. A cold trap is an area in our atmosphere that gets so cold that water freezes and falls back down. It's the primary reason our water hasn't floated off into space.

• Please consider asking that question on physics staxechange. You will probably find more people capable for such calculations there. – running.t Oct 27 '17 at 10:37
• For now I'll leave it here, but if I don't get an answer this week I'll make sure to try other exchanges. Thanks! – rclev Oct 27 '17 at 13:14
• I think you should link these "calculations" you keep referring to because I am unconvinced that green house gases are a determinate factor in atmospheric stability. To my knowledge planetary mass, distance from a star, and presence of a magnetosphere are bigger more critical factors. – anon Oct 27 '17 at 14:29
• @anon I apologize, but I think you misread my question or perhaps I can phrase it better. All those things you listed are much more important, but what I'm wondering is if the cooling effect of greenhouse gases in the upper atmosphere could have an offsetting effect on Jean's Escape and extend the length of time an atmosphere can survive on the moon. – rclev Oct 27 '17 at 16:01
• How does this differ from worldbuilding.stackexchange.com/questions/70898/… – Ville Niemi Oct 27 '17 at 17:17