Edit: To expand on the last claim a little, I was thinking of this: https://dothemath.ucsd.edu/2011/07/galactic-scale-energy/
The graph of Earth's surface temperature assuming 2.3% yearly growth in energy consumption is... illuminating. Basically, in a bit over 400 years, the surface temperature on Earth would reach the boiling point of water, not due to the complex effects of climate change, but simply because the amount of waste heat generated by energy production and usage will exceed the Earth's capacity to dissipate into space. Obviously disastrous temperatures would occur rather sooner. Unfortunately our societies hinge on constant economic growth, which, in turn, seems to hinge on growing energy usage.
Unless we build nuclear fusion reactors, which seems quite likely on the 400 year time scale you're talking about.
But this is not a problem- it's well known that nuclear fusion reactors on Earth would burn much hotter than the temperature at the sun's surface. The average temperature of the Earths surface can exceed the average of the suns surface no problem, as long as much of that is concentrated in small areas- namely, the spaces occupied by the reactors!
It could be used for carbon neutral or negative fuel production, for example, to keep things like planes in the sky and world travel cheap without harming the environment.
If anything -- it'd even make more sense for BTC companies to use solar since costs are a LOT cheaper.