But also unlimited cheap power to reduce the heat in the atmosphere, through some kind of worldwide air conditioning. Maybe with unlimited power we can finally control our weather through heating, cooling and redirecting ocean currents and whatnot.
Yeah, but no. Air conditioning and refrigeration produce localised cooling, but an overall heating effect thanks to inefficiencies. Worldwide air conditioning would dump even more waste heat into the atmosphere. Just as trying to cool the kitchen by leaving the freezer door open warms it, trying to cool the atmosphere with worldwide air conditioning will warm it even more.
The gp might have been thinking of more interesting methods of cooling - space sunshades, aerosols, massive creation of artificial snow... (not sure if the latter is a net heat loss)
Or you manage to store it somewhere. Thinking extreme here, we can get massive energy out of nuclear fission, what if we could revert it and put massive energy back into elements to do reverse nuclear fission. Or maybe convert lead into gold. And use it to create fuel to power our space trips.