Yeah I wonder the same thing - I keep getting told heat management in space is hard, but nobody discusses this inre the data centers. My understanding is one cooling mechanism is to just shoot lasers out into space (is this sci fi?) - I guess in that case you could just send energy back to your solar rigs, depending on wavelengths. TLDR: no idea

The whole thing is pie in the sky same as landing people on Mars. It's cool but if you look into deeper it doesn't make much sense and it's extremely challenging and on top of it all expensive as hell.

I understand that in earth based data centers, 30-40% of the power is spent on cooling. That's in facilities that can cool using conduction and convection to the outside environment.

I don't have any experience in this area, but it seems like for every square meter of solar panel you need about half that in radiator area. And depending on your orbit, these are probably not static things just sitting there, they need to be orientated correctly to work and their correct orientations will change over time.

The worry for me is the level of human maintenance required. The ISS has probably the biggest solar array around, and they send humans out to perform maintainance and repair on it multiple times a year. A decent size data center would need an order of magnitude more solar and radiators than the ISS, and so presumably would need even more maintenance.