If we turned the Earth into a black body and used all Solar radiation to run computers or move stuff around at the theoretical limit, we'd still need the surrounding space to radiate off the heat as our cold well. So the temperature would be at whatever that equilibrium condition is, but wouldn't steadily increase. The equilibrium condition could be all over the place and would be largely determined by the composition of the atmosphere.
For the record I'm not in favor of paperclipping the planet like this. If anyone was wondering.
>For the record I'm not in favor of paperclipping the planet like this. If anyone was wondering.
We should do this with Venus instead. It isn't doing anything useful at the moment, and is closer to the Sun than Earth. Mercury might be easier though.
That doesn't work quite the way you think. If you harness all the energy your planet will start to glow, first red, then white. Eventually becoming as hot as your star, at which point you stop gaining energy.
Unless they are somehow converting that energy to matter, the laws of thermodynamics mean that all that energy eventually becomes heat.