> I guess an issue could be heat exchange from a vacuum to whatever the cooling system is, but that's above my brain grade.

That's sort of the whole problem though. Whatever particles are around in a near-vacuum might be very cold, but there are also very very few of them. There just isn't anything to exchange the heat to. A vacuum is an insulator, that's how Thermos bottles work for example.

The problem with space being cold is that it’s also empty. You know how a windy day at 40 degrees out feels much colder than when it’s 20 degrees out but with no wind? Take that to its logical extreme. Things do cool down in space, but not by convection or conduction so it’s very slow.

Heat exchange in vacuum largely works with a different principle and is much, much less efficient. Without other molecules to transfer heat to, we're left with black body radiation. Lower efficiency means bigger radiators. It's basically trying to cool down by giving off infrared light.

Something that could be done with a small coolant loop through a river or a glorified AC on earth, requires large sail-like structures in space (sails because it maximizes the surface to throw out that thermal radiation).