Heat dissipation isn't as big a concern as it seems: the weight of the solar panels is significantly larger than that of the heatsinks you'd need per typical modern gpu
The cooling is not an issue for their current designs. Look at their AI1 Satellite specs. They clearly have the cooling figured out. The thing is that it's not a datacenter, it's a single rack. A single rack that weighs multiple tons.
You can figure out the weight of the thing based on the total power output, and "power to weight ratio" from SpaceX's own diagrams. Then look up how much it costs to launch per ton, and even look up what they are projecting it will cost with Starship. Even if they get costs down, it's still astronomical. I just can't figure out who would pay that much money to put a rack into space. There's no way the power savings are worth it. Unless you have some niche where you need your workload in space, I can't see the value at all.
It's not just the weight some outside groups have done the calculations and to dissipate the heat at the operating temperatures in the white paper without a heat pump to increase the radiator temp and thus efficiency requires a massive pump that would have to move nearly 69,000 kg of coolant per second continuously without fail.
You can figure out the weight of the thing based on the total power output, and "power to weight ratio" from SpaceX's own diagrams. Then look up how much it costs to launch per ton, and even look up what they are projecting it will cost with Starship. Even if they get costs down, it's still astronomical. I just can't figure out who would pay that much money to put a rack into space. There's no way the power savings are worth it. Unless you have some niche where you need your workload in space, I can't see the value at all.