The physics is quite simple and you can definitely make it work out. The Stefan Boltzman law works in your favor the higher you can push your temperatures.
If anything a orbital datacenter could be a slightly easier case. Ideally it will be in an orbit which always sees the sun. Most other satellites need to be in the earth shadow from time to time making heaters as well radiators necessary.
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.
You not only need absolute huge radiators for a space data centre, you need an active cooling/pumping system to make sure the heat is evenly distributed across them.
I'm fairly sure no one has built a kilometer-sized fridge radiator before, especially not in space.
You can't just stick some big metal fins on a box and call it a day.
If we run the radiators at 80C (a reasonable temp for silicon), that's about 350K, assuming the outside is 0K which makes the radiator be able to radiate away about 1500W, so roughly double.
Depending on what percentage of time we spend in sunlight (depends on orbit, but the number's between 50%-100%, with a 66% a good estimate for LEO), we can reduce the radiator surface area by that amount.
So a LEO satellite in a decaying orbit (designed to crash back onto the Earth after 3 years, or one GPU generation) could work technically with 33% of the solar panel area dedicated to cooling.
Realistically, I'd say solar panels are so cheap, that it'd make more sense to create a huge solar park in Africa and accept the much lower efficiency (33% of LEO assuming 8 hours of sunlight, with a 66% efficiency of LEO), as the rest of the infrastructure is insanely more trivial.
But it's fun to think about these things.
Put another way, 2 sq m intercepts 2600 w of solar power but only radiates ~1700 w at 350 k, which means it needs to be run at a higher temperature of nearly 125 celsius to achieve equilibrium.
It receives around 2.5kW[0] of energy (in orbit), of which it converts 500W to electric energy, some small amount is reflected and the rest ends up as heat, so use 1kW/m^2 as your input value.
> If we run the radiators at 80C (a reasonable temp for silicon), that's about 350K, assuming the outside is 0K which makes the radiator be able to radiate away about 1500W, so roughly double.
1500W for 2m^2 is less than 2000kW, so your panel will heat up.
[0] https://www.sciencedirect.com/topics/engineering/solar-radia...
You need enough radiators for peak capacity, not just for the average. It's analogous to how you can't put a smaller heat sink on your home PC just because you only run it 66% of the time.