mm wrote:

I've turned off the electricity to my water heater and it stays pretty
hot for 3 days iirc. And it would stay hot a lot longer if I weren't
using the hot water. The major thing cooling off the water is the
cold water going in when I use hot water.

A very clever timer and a well-programmed family might save significant
energy if it turned on a half-hour before the first use of the day and
turned off before the last use, an hour later, leaving itself entirely
filled with cold water for 23 hours per day.

Nick