If there were superheros that could violate the laws of thermodynamics at will, I would expect them to at least run the world on limitless clean energy.

It would probably only take a little bit of time to figure out ways to store the energy so that all of society could run without the superheros continuously working shifts and stuff: like maybe they just reheat a molten salt core from time to time, or fill up a high altitude lake with water upstream from some hydro plants.