The average temperature of deep space is approximately -270.45°C or 2.73 Kelvin), which is just above absolute zero. This baseline temperature is set by the Cosmic Microwave Background (CMB) radiatio...
Which is absolute nonsense, because vacuum has no temperature.
It's cold there because there isn't anything there.
So there is nothing to conduct or convect the heat away.
It's like a giant vacuum insulated thermos.
Is putting data centers in thermos' a good idea?
There is also no matter to wick the heat away.
https://en.wikipedia.org/wiki/Black-body_radiation
It has nothing to do with the movements of atoms, but just with the spectrum of photons moving through it. It means that eventually, any object left in space will reach that temperature. But it will not necessarily do it quickly, which is what you need if you're trying to cool something that is emitting heat.
plus you would have to insulate the servers from the sun...then have radiators like the ISS... i think its just way easier to run a server on the ground
If you had a thermometer that had no heat generation then yes.
If you have a resistor or other heat generating circuit then you need to have the needed surface area to radiate the heat away. If you don't, it will heat up. It's a rate problem.