The radiators are what need to be very hot. IIRC it works out to, order of magnitude, a similar area to the solar panels. These satellites would likely be placed in SSO, a polar orbit that precesses at the same rate that the Earth orbits the sun. So the fraction of time they see the sun would be very high. Cosmic rays are a little bit of an unknown, we don't know exactly how a commercial GPU running an LLM deals with cosmic ray radiation. I think the intuition is that it would be very little because a single bit flip in that vast array of matrix math and many times its result might not actually change any activations anyway.
I think the big problem with the idea is that GPUs have a failure rate and even if they didn't, they become obsolete. Most orbital DC plans are really more like flying server racks with no servicing in orbit. So when the GPUs die the satellite is a flying brick. All the power equipment, all the thermal equipment, all the comms equipment now depreciates at the same rate as GPUs. Very different economics from terrestrial DCs. And that's all assuming that you can launch everything up there quite efficiently. And the satellites take time to engineer but DCs are a more known quantity.