We have radiators on the ISS. Even if you kept the terrible performance of those ancient radiator designs (regularly exposed to sunlight, simplistic ammonia coolant, low temperature) you could just make them bigger and radiate the needed energy. Yes it would require a bit of engineering but to call it an "unsolved problem" is just exaggerating.

It's a solved problem. The physics is simply such that it's really inefficient.

> ... we'd need a system 12.5 times bigger, i.e., roughly 531 square metres, or about 2.6 times the size of the relevant solar array. This is now going to be a very large satellite, dwarfing the ISS in area, all for the equivalent of three standard server racks on Earth.

https://taranis.ie/datacenters-in-space-are-a-terrible-horri...

The gist of it is that about 99% of cooling on earth works by cold air molecules (or water) bumping into hot ones, and transferring heat. There's no air in space, so you need a radiator 99x larger than you would down here. That adds up real fast.