Short of shooting hot lava into space[0] we pretty much are because, once again, thermalization through radiation is governed by Stefan-Boltzmann's law and there's no way around that.
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.
Kinetic energy will end up getting converted to waste heat nonetheless.
> or bound carbon
This seems hard to imagine. We're dealing with waste energy here, so a very high-entropy type of energy. Bound carbon is low-entropy, so the conversion is impossible[0] unless we put that entropy elsewhere.
As an analogy, consider a fridge: It brings your food from a high-entropy (high-temperature) to a low-entropy (low-temperature) state but in order to do that it also has to produce waste heat (entropy) on the outside.
[0]: https://en.wikipedia.org/wiki/Second_law_of_thermodynamics