The whole ship would be radiators, or absorbers, to then put into hyperspace "radiators." There is of course no reason to suppose that the hyperspace part is "outside," it might be in the center as hyperspace is not in our usual dimensions anyway.
Still, that is massively breaking physics. In general, I like space combat ideas where you pick a few things to break, and try to hold them to those as much as possible (say FTL drives).
In fantasy "SF" like star trek, they can radiate via "subspace" radio, presumably. Of course if you can broadcast in hyperspace/subspace, you can likely receive in that same space. So you stop radiating IR to a point, and replace it with detectable "subspace" radiation---which might be detectable at vastly greater distances, BTW, if it is the space used for FTL. So as a work around, it's a bad one.
Also, even if you collect "excess" radiation for mitigating using some made up tech, the hull is still shirtsleeve temp for the crew. A small ship is easily detectable at the distance of our moon with current, small, IR telescopes that could automatically scan the complete volume of space around the ship in a short time frame.
You cannot cool the hull to be equal to background if people are inside.
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