My guess would be that it involves the amount of adsorbed gasses in cold water as opposed to hot water.
Heating the water over an extended period drives the adsorbed gasses out. So cold water will have more gasses adsorbed in it.
Adsorbing a gas in water lowers the freezing point. We’ve all seen this with a can of coke that’s very cold but still liquid, and when you pop-the-top and let some co2 out it immediately freezes.
Warm water makes for less cloudy ice cubes.
That's pretty much what I thought as well, mainly because of the clarity of the ice you get with hot water, as opposed to cold, although I think the speed of freezing also has something to do with how cloudy ice is.
Stand back folks! I'm going to attempt ... science!
I like your answer best.