I think it depends if our predictions for the half life of a proton is correct. DieCommie is right every thing will eventually become low energy photons in the heat death theory.
Might there be an cosmological era when superconductivity or condensates predominate? In the lab they seem the most distinctive phenomena at low temperatures.
It depends. If protons decay there will be no matter to be superconductive, but if they don't then via quantum tunneling all matter will eventualy behave as liquid.