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Global warming isn't caused by dumping heat into the atmosphere. It's caused (very simplified) by changing the planet's properties such that it's thermal equilibrium, the balance between sun's radiation heating it up and radiatively losing heat to space, lies higher. Mankind's waste heat (~10^12 W) is utterly miniscule compared to sun's energy delivered to earth (~10^17 W).

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I think that is precisely OP's point: on the long term, solar & friends are the only things that matter. If we get unlimited cheap power, we can only ever use it to generate an 'utterly miniscule' fraction of energy compared to what's available from solar because if you want to add a meaningful contribution to the energy content of the planet, you'll simply cook yourself, not from chemical global warming, but from thermodynamic waste heat.

This. Carbon Dioxide in the atmosphere is basically the earth's thermostat. The amount of energy coming from the sun is constant. It must be balanced by the thermal radiation leaving the upper atmosphere. But the more CO2 there is, the higher the elevation of that thermal radiation and the higher the surface temperature.

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