There are even commercially available prototypes of that vacuum cooling technology, if you want to perform your own experiments with that concept: https://www.amazon.com/Thermos-Stainless-Ounce-Drink-Bottle/...

I wonder if there should be levels of "in theory". Yes theoretically black body radiation exist and well stuff cools down to near background radiation via that. But the next level is theoretical implementation. Like actually moving around the heat from source and so on. Maybe this could be the spherical cow step...

Reminds me of the hyperloop. Well yes, things in vacuum tube go fast. Now does enough things go fast to make any sense...

Serious question: how in theory?

I’m under the impression you need to radiate through matter (air, water, physical materials, etc).

Is my understanding of the theory just wrong?

You can radiate the excess energy away on the non-sun facing part on Earth almost just as well..., though corrosion is an issue.

It's not the Sun..it's the lack of medium.

Yes. And it's an absolutely terrible way to get rid of heat. Cooling in space is a major problem because the actually effective ways to do it are not available.

There's no air and negligible thermal medium to convect heat away. The only way heat leaves is through convection from the extremely sparse atmosphere in low Earth orbit (less than a single atom per cubic millimeter) and through thermal radiation. Both of which are much, much slower than convection with water or air.

Space stations need enormous radiator panels to dissipate the heat from the onboard computers and the body heat of a few humans. Cooling an entire data center would require utterly colossal radiator panels.