Thermosphere is a layer of the Earth’s atmosphere from about 95 km to 600 km. It is named ‘thermosphere’ because its temperature increases with altitude. Temperature in the thermosphere can reach 2500°C.
Flat-earthers question this fact a lot:
“If temperature in the thermosphere can reach 2500°C, then how is it possible for human to travel to space? Not to mention that many satellites —including the ISS— are in the thermosphere.”
Short answer: air density in the thermosphere is much, much lower than at the surface of the Earth.
The mass of Earth’s atmosphere is concentrated on the lowest layers. 90% of all mass is below 16 km. 99.99997% is below 100 km. The thermosphere itself begins from 95 km upwards to about 600 km, and only 0.002% of the mass of Earth’s atmosphere resides in the thermosphere.
Heat transfer is directly proportional to difference of temperature and mass. Air molecules in the thermosphere may have 10× higher temperature than at the surface of the Earth. But at the same time, its density is 10.000.000.000.000× lower. As a result, it has less heat energy per unit volume compared to our bodies. We would not feel warm in the thermosphere, and a normal thermometer might indicate below 0°C.
The situation is not unlike if we get hit by splattering hot frying oil. Usually it is not a big problem. The splattering oil has the same temperature as the boiling oil in the pan: it can reach 200°C/400°C! But at the same time, it has very little mass, unlike the oil in the pan. That’s why it is usually not a big of a problem. At least not as big as if we decide to submerge our hands in the boiling frying oil to compare the outcome!
So, yes, temperature in the thermosphere is not a problem for space flights.