oh you should google for info--i do remember reading that someone did actually perfome a series of experiements about hot/warm/cold water and freezing time..

hot water does freeze marginal faster, --but more important it freezed clearer.

air is an insultator. (a pretty good one too) most of the 'warmth' of clothing is based on how good the clothing is at traping air around our body -while still letting moisture evaporate.

air trapped in water --and cold tap water is often 'aerated' has lots of air. hot water has less (especially water that has been heated (boiled) and let to set for 2 or more minutes (so its cools a bit, but it's still very hot)

with out all the air, the water freezes 'evenly'(and faster,(no air to insulate/retard the freezing process) and you have smaller chunks of the milky white ice in the center of cubes/block (which is white because of small bubbles of air) and the clear ice can freeze colder.. (since there isn't downward limit to how cold ice becomes.

'ice companies' use distilled water for freezing to make large clear blocks of ice for sculptures.