I'd in no way describe myself as an "expert" - just "interested". However my interests are varied, and this results in understanding of a wide range of principles.
As I mentioned with regards to carnot cycle in stirling engines, a less efficient conversion process utilised in extracting energy from the excess thermal energy could result in significantly higher energies being removed, increasing the effectiveness of the complimentary technology, in terms of removing heat energy. But the primary system - for anything "significant" is going to be ... intense. I'm currently unable to envision viable solutions beyond "increase surface area". This is naturally problematic in as much as it increases vulnerable surface area, and gives more places for problems to actually happen - to assume it pumps liquid in a grid array, then each intersection on that needs a valve to prevent it bleeding coolant into space if it's breeched... increasing size increases mechanical complexity, and gives rise to more things that can go wrong.... Simple systems tend to be the most effective, the simpler the better... A system isn't perfect when you run out of things to add, it's perfect when you run out of things to remove. Preferably that simple it operates on the laws of physics itself - like the metamaterial lighting - and thusly failure quite simply isn't an option. Ofc, not everywhere needs lights - especially constantly. Although some sort of iris or shutter could serve to solve that. But even using the entire exterior hull it's unlikley to remove significant quantities.
As well as the biological thermal output with mass habitation, I predict various industrial mining processes to generate vast amounts of heat. It might be possible to render asteroids to smaller, processable chunks with resonance, these chunks should easily powder by mechanical means - various techniques can sort all at relatively low temperature - but things like smelting iron are really going to require some serious dissipation. And we really need to be doing things like that up there, or we've got no chance of getting the bits together to build places for us to be. There's too much required to lift form the surface - it's too heavy, would take too many trips. By the time the mulitple trips are complete, our grandchildren would be dead. And it would of raped the Earth bare in the attempt. Taking it from up there can happen a lot faster if you do it right, impacts the Earth minimally, and the process of which will open up the abundant resources of the universe for harvest. Almost everthing is ready for that to happen - some things just need a little tweak... Thermal dissipation is definitely one of these things. In the case of mining, it should be possible to use a modular design where a heated crucible is then removed, and it can be disconnected from the facility to prevent it bleeding it's heat. The setting of that into a usable material is likely to require a slower gradient than space would naturally provide so some of that thermal energy can be recycled there... That and a few other industrial processes I predict to be problematic in this regard.