Sure, possible. But the timescales involved are daunting, as is the energy/tech required to shield a blackhole with sometime so efficient that the temperature gets down below 1 kelvin.

It's not all that much energy for the timescales involved, you'd be better off just putting say an acre of solar panels in orbit around the sun.

Tiny blackholes are amazing efficient engines for turning mass into energy, once small enough they could be quite a power plant and not picky about what you feed them.