Every single satellite has sufficient cooling for its power production, otherwise they would be frying. Waste heat from a GPU is not materially different from waste heat from an amplifier. That's not cooling entire racks, but I don't think anybody talks about putting entire racks in space anymore.
I'm very much pro nuclear, but a solar cell in a sun synchronous orbit is pretty great too and eliminates most battery requirements
I very much doubt the economics of this makes sense, but I don't think a lot of your criticism is valid.