The same problem crops up when you're talking about moon bases and so on - you've got the same problem of venting heat from an ecosystem into a vacuum. For that situation, one of the solutions that got designed out was to basically spray an oil mist across a gap, catch it, and recycle it into the cooling system. As a fine mist, the oil has a colossal surface area compared to its mass, and all that surface area can radiate heat off into the vacuum.

So... scale that up? I realise it's a hell of a leap, to go from human-scale to humanity-scale, and I don't know exactly what it would need to look like, but limitless energy is a hell of a springboard.