Under what is currently understood about the universe, the following could take place:
If for some reason the universe were to be leading for increase temperatures the overall temperature of the universe would increase; particularly in greater concentrations of mass [Galaxies and clusters of galaxies]; the temperatures would be more likely to be greater in local sectors of the universe given how it's currently understood the expansion of the universe; galaxies will still drift apart but the very "spots" of mass that would be left isolated due to the expansion would be hotter. In a universal scale it probably would not make much difference given the vast distances that would [and do] separate everything.