We already have hot and cold water distribution. Most Swedish homes have central heating using hot water radiators, and central cooling is now starting to become a thing here. Any sink in a house has hot and cold water.

It’s absolutely possible to tie into this by making use of recirculation systems where you have constant flow of hot/cold water and every household source of heat or AC unit for cooling can tap into it (pun intended) to feed back generated heat or contribute to cooling. Then you use storage systems (thermal mass or thermoelectric generation) for the excess.