What is the temperature of air in the upper part of our atmosphere?
I read somewhere that it is of the order of 1000 K, but then, why is it cold there?
My question is different from the aforementioned question because it considers the outer atmosphere, and the various interactions occuring there, something which is completely out of context in the other question.
So this is actually a quite true effect and can seem very confusing!
Our atmosphere has some very nice easy-to-understand properties, for example both the density of the atmosphere and therefore the pressure decrease exponentially as you get further away from the surface. But temperature is not one of them! In fact, as you go up higher in elevation, temperature slowly decreases roughly linearly until you get to a height a bit above Mount Everest. Beneath this region, the entire familiar "atmosphere" that you know and love, including most of the cloud types you know and love, you is called the "troposphere", and it ends at this height a little above Everest, where normal airplanes fly, at an elevation called "tropopause", because the temperature actually stops going down and starts going up (therefore it is roughly constant, or "paused", for a certain distance in the middle).
The reason for this heating in the next layer, the "stratosphere", is that the Earth's warmth is not the only source of heat in this system! Actually, the ultraviolet rays from the Sun's light get absorbed by the ozone in the stratosphere -- so if you've heard of the depletion of Earth's "ozone layer" by "CFCs", that's where this has happened. Then there is another thin layer of Earth's atmosphere where the temperature again decreases, the "mesosphere", but we're getting to a really important part -- Earth's "ionosphere", which includes the mesosphere as part of it. In this space, even more energetic light is actually breaking apart atoms into a cloud of ions. These clouds are occasionally responsible for the "auroras" seen around the poles, in combination with the solar wind and magnetic fields of the Earth. And since this happens by the absorption of the Sun's rays, the temperature also starts to increase in the "thermosphere", the main part of the ionosphere where this is happening.
The thermosphere gets up to a really hot temperature towards its outside!
What you have heard is that if you went to these upper layers of the thermosphere, then it would have a high temperature, but "it would feel cold." And the reason for that is that temperature just tells you "which way would heat be transferred between these two objects?" but your skin tells you something different, "is heat-energy leaving my body or entering it?"
Let's suppose you were in shade from the Sun. Due to the Stefan-Boltzmann law your body radiates heat as infrared light into its surroundings all the time, maybe a kilowatt of power or so, at a rate proportional to $T^4,$ where $T$ is the temperature in absolute units. Your body temperature is about 310 K, a warm room is 295 K, so the difference in heat flux is about $(295 / 310)^4 \approx 82\%$ of this infrared radiation is presumably getting returned to you. Out in space this probably drops significantly. So there is much more heat leaving your body.
Yes, every particle that hits you in the atmosphere will impart a lot of energy which will hopefully get absorbed as thermal energy -- but the density of particles in the atmosphere has been decreasing exponentially, as you'll remember, so that at this height there is just not enough of these hot particles to create the sort of heat flux you need to avoid this cooling-by-radiation.
The Sun, of course, changes a lot of this because it is even warmer in the upper atmosphere before these things have absorbed its light, so that if you were spinning around in this part of the atmosphere possibly the warmth of the Sun would make it feel warm again, kind of like when your back has gotten cold around a campfire so you turn around to warm it up again.
