But isn't space like a heat bath at -273° C? I think there's a finer point one or both of us is missing.
Cooling is much easier on the ground.
In space you can only dissipate heat by radiation. In an atmosphere you can also transfer excess heat into matter that you can carry away and dump elsewhere, using conduction, convection, and forced circulation.
For a concrete example, consider Google's average 2011 power consumption of 258MW. What happens if they do all that in a huge server farm in space? Assume the exterior is a perfect black body and the interior is a perfect thermal conductor.
From the Stefan-Boltzmann law, for the equilibrium surface temperature to...
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