Does water temperature matter to cats?

For most cats, yes, in preference more than in health. Many cats prefer cool water over water that has sat out and warmed to room temperature, which is part of why a fountain (whose movement keeps water a bit cooler and aerated) can nudge a reluctant drinker to visit more. There is no health requirement for a specific temperature. If your cat seems to avoid her bowl by afternoon, try refreshing the water once more during the day rather than assuming she needs a new bowl or fountain altogether.