Why is it severely cold high up in the atmosphere?

"In the upper part of the atmosphere ... one feels severe cold" - I guess this statement requires some qualification, as this depends on whether one is exposed to sun radiation.

In the upper atmosphere (thermosphere starts at about 85 km), the air density is negligible for most purposes, and I don't think anybody has ever been at such altitude (without a spaceship or a spacesuit), and if people found themselves there, their immediate problems would be lack of oxygen and blood boiling, not cold.

As we go up in the atmosphere , the number of molecules per unit volume decreases . The quantity of heat per unit volume or the heat density is low . But the translational kinetic energy per molecule is quite large. As the kinetic temperature is the measure of translational kinetic energy, so the kinetic temperature is quite high in the upper atmosphere but one feels severe cold due to low heat density.

The sensation of "cold" is really a measure of how rapidly a body is losing heat.

The thermosphere (extreme upper atmosphere) does have a high kinetic temperature, and its molecules do transfer heat to any cooler body they collide with. But since the density of the thermosphere is extremely low, the energy they transfer is also very low.

A body loses much more energy than it gains from the thermosphere, thanks to radiation exchange with deep space, which is at about 3K (-270C).