Cooling is relatively easy, you just need radiators which are passive, and essentially reduce to a launch cost penalty. You are right that they can't be serviced, but that is missing the point of orbital data centers. The whole point is that you can build hundreds of thousands of these in a factory and launch them in a scalable manner. The power, cooling, etc. comes for "free". In the long run, as the cost of the chip, launches, etc. goes down, orbital data centers will scale better terrestrial ones.

As a side note, I don't understand why I keep seeing these wrong arguments on HN repeatedly. Like everything mentioned in this thread can easily be fact checked. Radiative cooling is solved, launch costs are going down, so power costs will pay themselves back very quickly, etc.

You can argue about specifics, like chips will get more sophisticated + power efficient and fabrication will be the true longterm bottleneck, or SMRs/fusion could reduce energy bottlenecks, but talking about cooling as if convective cooling is the only option is just nonsensical.