Radiative cooling isn't as big of an impediment as people think. It's part of the reason why a desert that's 120F+ during the day gets so cold so fast unless there's cloud cover to radiate back.[1] IIUC correctly, the theoretical maximum is over 400 watts per square meter, and existing tech can achieve 80-90+% of that. It's an engineering challenge, but no more than creating reusable rockets. The real challenge is building a reliable convective system from the heat source to the radiating mechanism, and just the general problems of building a compact package for delivery that then unpacks and orients itself once in orbit. No new science is required, and you can pencil things out today the same way Musk did when penciling out the economics of building a reusable rocket.

[1] Convection effects are also involved, but that cuts both ways as the air is also radiating back at you. A significant fraction of the net cooling is pure radiative.