Technology

Basically they'd need about as much in radiator fin surface area as they would have in solar panel area. The ISS has 8 solar array wings, 35m x 12m, that can produce about 30 kW each, or 240 kW total, in sunlight (which is only half the time). The ISS has a complex cooling system, but relies on 4 radiators about 3.1 m x 13.6 m to reject up to 14 kW of heat each (56 kW total) for cooling the solar arrays themselves. The main cooling system uses 6 radiators, each 23.3 m x 3.4 m, to reject 70 kW of heat (from this report it sounds like each radiator may be capable of rejecting more than 1/6 of the heat but that the system as a whole needs to be kept under 70 kW of heat rejection).

So that seems like about 650 square meters of radiators can provide about 120 kW of heat rejection.

Today, a 72-GPU Blackwell server is 130 kW in a single server rack. The next generation rolling out now has 72 Rubin GPUs in a 230 kW server, in a single rack. And that's not even a "data center." That's just a single (albeit very powerful) server. How many can you string together, with networking equipment beaming data connections back down to the ground, before the ratio of solar panels and radiators to the actual ship size becomes unworkable?

That said, it's technically possible, especially if you can radiate the heat at higher temperatures than the ISS does, as the Stefan-Boltzmann law shows that the hotter the radiator, the more heat it can reject. Just completely infeasible from an engineering and economical standpoint, for any data center that hopes to be relevant in an age of 100+ MW data centers.