A body in the Earth’s atmosphere is usually heated by the Sun, the IR radiation reflected from the surface, and the gas molecules around it. As the altitude increases, temperature increases as you have mentioned. But the density decreases with altitude as well. So when you’d shoot up yourself to the thermosphere, you will be in a very less dense area. There will be not enough gas molecules surrounding you to conduct heat. This is why the thermosphere won’t heat you up! In addition to this, your body will also radiate away the heat inside you. Due to lack of conduction, you will eventually start feeling cold in the thermosphere.
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