So it's all gases at greatest density will be doing the same thing around the planet at the same time (*) and as these change with
differences in density
in the play between gravity and pressure and kinetic and potential from greatest near the surface to more rarified, less dense and absent any kinetic to write home about the higher one goes, then, energy conservation intact, the hotter will rise and cool because losing kinetic energy
means losing temperature, thus cooling they which began with the closest
in density and kinetic energy as a sort of band of brothers near the surface will rise and cool at the same time whereupon they'll all come down together colder but wiser that great
heights don't make for more comfort and giving up their heat will sink displacing the hotter now
in their place when they first went travelling.