So is the plan is to use a heat-pump to cool the computers while getting some waste-product as hot as possible, and then eject the waste product? Or perhaps rather than ejecting it, the heat could be put into a large surface-area heat-sink thing to just radiate the energy black-body-style...

I think ideas like this are fair and reasonable if we have to have a data centre in space (for example, if we wanted people to live indefinitely on a space-colony or something like that). But its pretty clear that no plan will ever be anywhere near as good as what we can do on the planet's surface.

Building and operating these things on the Earth's surface is already expensive and resource intensive. And doing it in space is going to be a lot worse.