The Heat Pump would take one Heat from ship to nother. So you could have Combat Ships, with Heat Sinks but with little to no Radiators. (Yea, better word.) ANd so you can multiple ships service by one Support Ship cooling them off.
FACs may be weaken quite a bit with heat. Though if they could return to a Support Ship where they can off load their Heat, this would mitigate it.
The Stealth Tech themselves would generate heat, and would already doing its job at lowering the heat profile of the ship regardless. This wouldnt really need to be changed mechanically. Its numbers would need to be tweaked. This would make Stealth maybe weaker, but more interesting as it'll be limited by how long it can be an oven.
This may also require to generate an ambient heat map of a given system. It may be fast enough to know how warm the dead of space is compared to the distance (and stats of the star). The further away you are, the more efficient radiators are.