That is just a load of bs. Heat pumps do not operate efficiently at high temperatures, and they only add more heat to the circuit. You cannot generate energy from the temperature difference, because then you would slow heat transfer significantly while generating an insignificant amount of power.

It has already been calculated, and radiators are a really big issue for "space datacenters". Even with our current cooling technology advancements. Server hardware needs to be kept at a cool temperature (ideally not higher than 50°C), and most importantly, it needs to be constant in spite of very variable hardware load. That is really difficult to manage in space, and an issue that needs to be considered even for our non datacenter satellites.

But even if cooling was trivial, space datacenters make absolutely no sense.

For starters, it wouldn't be possible to put any server in the market up there. Chips are very vulnerable to the radiation in space, which is why space CPUs are stupidly expensive and way slower than earth CPUs. They need to use less efficient litographies, with very special shielding that isn't commonly available. The sheer compute and memory density of our current servers would be impossible to properly shield, even if we ignore the cost. ECC RAM and ZFS pools for drives would very quickly stop protecting your server from errors, since the bit flips would be too common, and your computations would often be incorrect.

If you ignore both cooling and space radiation, you still have the issue of accesibility. Datacenters have people always coming and going, because hardware needs maintenance. Sometimes you want to upgrade the server, change the connections, add or remove hardware, and of course, you need to replace the parts that break over time. Hardware becomes old really quickly, especially for the compute intensive workloads that are planned for those "space datacenters".

Datacenters are kept fast and competitive through constant upgrading of the parts. Compute intensive servers also churn through parts very quickly, because even at 50-60°C temps, keeping hardware at 100% utilization isn't the best. This is further exhacerbated by temperature fluctuations, which can prematurely kill the silicon.

Like someone else mentioned in another comment, Microsoft already tried dumping containers with servers into the ocean, and putting wind turbines on top. That's free cooling, very stable temperatures, and free energy. Even if it was a success in every measure, Microsoft dropped it because it wasn't accessible enough, which made it unusable for any real usecase.

The truth is, datacenters are a market where cost is very important, and solutions are already very competitive. Putting a datacenter in orbit would be stupidly costly, even if you could fix all the issues mentioned. Free electricity does not offset those costs, and that's without taking into account the cost of the rockets for putting the datacenters in orbit.

TL;DR: There are so many issues and extra costs, even when ignoring cooling, that make datacenters in space a stupid thing to even consider.

And before you say I'm not an engineer and I don't know what I'm talking about, server infrastructure is my field. I've worked with datacenters, maintained server stacks and I myself have worked on those cost calculations. I know what I'm talking about.