That's not a new problem that no one has dealt with before. The ISS for instance has its External Active Thermal Control System (EACTS).
It's not so much a matter of whether it's an unsolvable problem but more like, how expensive is it to solve this problem, what are its limitations, and does the project still makes economic sense once you factor all that in?
The ISS consumes roughly 90kW. That’s about *one* modern AI/ML server rack. To do that they need 1000 m^2 of radiator panels (EACTS). So that’s the math: every rack needs another square kilometer of stuff put into orbit. Doesn’t make sense to me.
It's worth noting that the EACTS can at maximum dissipate 70kW of waste heat. And EEACTS (the original heat exchange system) can only dissipate another 14kW.
That is together less than a single AI inference rack.
And to achieve that the EACTS needs 6 radiator ORUs each spanning 23 meters by 11 meters and with a mass of 1100 kg. So that's 1500 square meters and 6 and a half metric tons before you factor in any of the actual refrigerant, pumps, support beams, valve assemblies, rotary joints, or cold side heat exchangers all of which will probably together double the mass you need to put in orbit.
There is no situation where that makes sense.
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Manufacturing in space makes sense (all kinds of techniques are theoretically easier in zero G and hard vacuum).
Mining asteroids, etc makes sense.
Datacenters in space for people on earth? That's just stupid.