Cold tap water is fine, as long as your not doing such a big water change that the temperature of the whole tank drops right down by like 5-10*C.
I've found no problem at all doing water changes smaller than 50% with cold tap water.
For water changes of or bigger than 50%, I use warmish water from the shower, or put some boiling water from the kettle into the buckets of new water. Just so the temperature change isnt huge and too fast.
Cold water changes even help some fish to breed .
Really I don't think it's something to fret about too much, I'm sure some species of fish can take big and fast drops in water temperature, I just feel safer babying my fish lol .