Less gas means less retained heat.
so more gas means there should be more heat, right?
this is the implication of what you have said. contraposition, if you wish to be logical, but you do seem incapable of that.
Actually the thin air at high altitudes is really cold because it's far away from any ground which heats up when the Sun shines on it. Presure also has an effect on temperature, lower presure cooks things down while higher pressure heats things up.
so now the sun heats the ground, which heats up the air? that makes no sense, the sun should be heating the air. you're just admitted that the earth's heat comes from the ground, and yet you still rely on the sun. how?
i think you'll find pressure increases as temperature increases. learn a little math. pressure is a consequence of heat, not a cause.
Sunlight generally passes right through air without much interaction and so air doesn't convert much of the Sun's light into heat.
so the poles should be plenty warm, by that logic.