Unlimited energy doesn't free us from the consequences of thermodynamics. Geoengineering doesn't help us. Where we generate the energy doesn't change anything if it's
used here on this planet.
There are literal physical limits here that can't just be handwaved away by space magic. Higher energy use in a finite spherical volume fundamentally results in increased temperatures when your only way of getting rid of that heat is radiation (and not convection or conduction). And we can't just beam that heat away with space magic either thanks to entropy.
Thermodynamics gives us no tools to deal with this problem outside of increasing the spherical volume of Earth (and therefore its surface area).