Space is a vacuum. i.e. The lack-of-a-thing that makes a thermos great at keeping your drink hot. A satellite is, if nothing else, a fantastic thermos. A data center in space would necessarily rely completely on cooling by radiation, unlike a terrestrial data center that can make use of convection and conduction. You can't just pipe heat out into the atmosphere or build a heat exchanger. You can't exchange heat with vacuum. You can only radiate heat into it.
Heat is going to limit the compute that can be done in a satellite data centre and radiative cooling solutions are going to massively increase weight. It makes far more sense to build data centers in the arctic.
Musk is up to something here. This could be another hyperloop (i.e. A distracting promise meant to sabotage competition). It could be a legal dodge. It could be a power grab. What it will not be is a useful source of computing power. Anyone who takes this venture seriously is probably going to be burned.
When one does the math on the operating temperatures of regular computing equipment that we use on Earth, how much heat it generates per watt, and how fast it would need to sink that heat to allow for continuous operation, one gets surface areas that are not impossible, but are pretty on the high end of anything we've ever built in space.
And then you have to deflect the incoming light from the Sun which will be adding to your temperature (numbers published by private space companies regarding the tolerances of payloads those companies are willing to carry note that those payloads have to be tolerant of temperatures exceeding 100° C, from solar radiation alone). That is doable, you could sunshield the sensitive equipment and possibly decrease some of your thermal input load by putting your craft out near L2 which hangs out in the penumbra of Earth. Still a daunting technical challenge when the alternative is just build it on the planet with the technology and methods we already have.
The Solar Load is Directional: Unlike a terrestrial atmosphere where heat is omnidirectional, space allows for "shadow engineering." A simple multi-layer insulation (MLI) sunshield can reduce solar flux by orders of magnitude. We do this for the James Webb Space Telescope to keep instruments at 7K while the sun-facing side is at 380K. For a data center, you don't need 7K; you just need to keep the "dark side" radiators in the shade.