A satellite as a whole will come to thermal equilibrium with space at a fairly reasonable temperature, the problematic part is that the properties of electricity make it easy to concentrate a good part of the incoming energy in a small area where the GPU is. Heat is harder to move than electricity and getting that heat back out to the solar panels or radiators requires either heavy heat pipes or complex coolant pumps.
If it had the same data center to rock ratio as earth, it would just end up being earth in the end, and earth doesn't seem to be wanting to stick to its equilibrium either right now
2 * pi * r^2 * L / (4 * pi * d) * (1 -a) = 4 * pi * r^2 * sigma * T^4
As you can see there are pi*r^2 on both sides of the equation, the surface area to cross section ratio of a sphere doesn't change as it gets bigger and so the equilibrium temperature doesn't change no matter how big the sphere is. (d is the distance to the Sun, nothing to do with the sphere itself).