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Presumably superconductors are a given at that level of technology. But also at megastructure scale, we could easily talk about very exotic energy transfer methods. Mirrors, microwave transmission antennas, kilometer wide conduits of highly conductive “ground” material, large scale production of fusion fuel, maybe usable power from heat difference is such an efficient process at any scale that the sphere just has a hot side on the inside (towards the sun) and a cold side on the outside (towards cosmic background) and anyone who needs power just patches in a heat pipe to the inside surface.
Actually there’s a lot there on that last one. Large efficient power plants could be built anywhere where people needed them hooked with big heat pumps into the inner surface and outer radiator surface, smaller applications could just hook into the inner surface and radiate heat passively and let the climate control deal with it. Rogue energy thieves could be tracked down by scanning for unregistered cold spots on the inner surface.
If you only put distilled water in it it really doesn’t seem like an issue