That is the measured air temperature, but it isn't used the way we normally think about it. At very high altitudes, the atmosphere is very sparse (i.e. very low pressure). There are not very many molecules of air, but those few do get hit with a lot of ionizing radiation, meaning they have a lot of energy.

It would not feel warm to you though, it would feel basically like space.

This is a poor analogy, but consider the difference between a single drop of water hitting your skin at high speed, versus a slow moving wave of water going over you. The drop has more energy, and if you just measured its 'speed' it would be higher than the wave.