These data centers are solar powered, right? So if they are absorbing 100% of the energy on their sun side, by default they'll be able to heat up as much as an object left in the sun, which I assume isn't very hot compared to what they are taking in. How do they crank their temperature up so as to get the Stefan Boltzmann law working in their favor?
I suppose one could get some sub part of the whole satellite to a higher temperature so as to radiate heat efficiently, but that would itself take power, the power required to concentrate heat which naturally/thermodynamically prefers to stay spread out. How much power does that take? I have no idea.