Is the air temperature constant at elevations above 20,000 feet? Antarctica could it be far colder?

The ground is warmed by sunlight and air is warmed when it touches the ground. Weather stirs the air so warmth is spread up and down and around a little, but air that does not touch the ground has a poor chance of getting any warmth. So the temperature drops with altitude up to a few hundred feet, and then it drops very slowly above that level. That's why mountain tops are snowy even in summer.

Then you have wind. The jet stream is an electric motor driven by current from the sun, the same current that powers the northern lights. It might move away from its nominal path to carry cold air down into USA almost to the Gulf Of Mexico. And it might not.

So no, the air temperature is not constant at all, and not predictable in most cases.