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.
That specific aspect is NOT true in space because there's nothing stopping thermal radiation.
Now you're correct that you can't remove heat by conduction or convection in space, but it's not that hard to radiate away energy in space. In fact rocket engine nozzle extensions of rocket upper stages depend on thermal radiation to avoid melting. They glow cherry red and emit a lot of energy.
By Stefan–Boltzmann law, thermal radiation goes up with temperature to the 4th power. If you use a coolant that lets your radiator glow you can conduct heat away very efficiently. This is generally problematic to do on Earth because of the danger of such a thing and also because such heat would cause significant chemical reactions of the radiator with our corrosive oxygen atmosphere.
Even without making them super hot, there's already significant energy density on SpaceX's satellites. They're at around 75 kW of energy generation that needs to be radiated away.
And on your final statement, hyperloop was not used as a "distraction" as he never even funded it. He had been talking about it for years and years until fanboys on twitter finally talked him into releasing that hastily put together white paper. The various hyperloop companies out there never had any investment from him.
Not necessarily. There are many modern thermos "cups" that are just a regular cup, except with two layers of glass and a vacuum. Even the top is open all the time. (e.g. https://www.ikea.com/us/en/p/passerad-double-wall-glass-8054... )
It's still good enough to keep your coffee hot for an entire day.