Provided most energy ends up as waste heat, not as/in stuff, I suppose (leaving aside doing waste heat intensive things off planet and dropping products back to earth etc.).
Managing heat with purely radiators (i.e. no need to dump hot matter into space to lose it forever) is… challenging at scales required. Not saying it can’t be done, but it’s a long shot.
Yes, purely radiating away heat might be tough. That said, 400 years at 2% is more than a factor of 2,500 - I'd expect some quite substantial changes to go with that as far as industry and society are concerned. For example, a lot more energy use might not be waste heat but creation of stuff or waste being high energy energetic radiation.
Your main point might be real, but until we manage to make it work around 0K, i'd have a hard time to believe a carnot engine can have an efficiency close to one. I think current "future" tech aim for something like ~50% (theorical) efficiency, and that's with a _very_ wide temperature differential that would put a real strain on materials.
