Dynomight realized that when we let a bathtub drain, a lot of heat energy goes into the sewers to be wasted. Running the numbers in Britain suggests one might save more than 3% of an energy bill letting bath and shower water sit in the tub until it cools off.
It's also interesting to quantify things in terms of money. If we use the new (October 2022) UK price caps, it costs something like £0.28 to heat the water for a bath or shower. So, scavenging the heat would save around £0.13 each time. That's assuming you heat your water with gas. If you heat your water with pricey electricity, you should triple those numbers.
Not sure this would make cool yet humid British homes feel nicer to be in, even if the thermodynamics of it all work out. Assuming its laws prevail beyond that green and pleasant isle, the same goes in the U.S., if not the exploding cost of energy to consumers.