I never questioned it.
Space is also extremely cold, and if it's as dense as Musk cooling won't be an issue.
The ISS doesn't have problems staying warm, it has problems cooling off.
It does say he's planning an AI sun, I'm guessing that's the temperature you need to run at for radiation to work.
And if you accept that the duty cycle of the AI+Starlink satellites will be less than 50%, it would be much better to build the data centers in random deserts and wastelands on Earth and use the Starlink network to talk to them.