I sorta have running hot water.
I do have a hot water heater. but 10 years ago it became heavily limed up. Not sure if you know about hot water heaters and what makes them leak. The mineral deposits on the inside of the tank get thicker and thicker over time until the fire has to run constantly to get the water hot. The lime acts like insulation preventing heat transfer into the water. Problem is, when the fire runs non stop, the metal overheats and begins to oxidize at an accelerated rate. Then you get a hole and a leak.(this is why stainless water heaters are kind of a waste of money)
Anyway, ten years ago I noticed my hot water heater was running non stop and the water took forever to heat up. So to make it last longer, I turned the temp of the water heater WAY down and reduced the gas pressure to the water heater gas burner.
The result is that I have warm water, not hot. But ten years later and i still have a water heater that doesn’t leak. I expect I could get another 5 years out of it with the current settings I have on it. had I not changed the settings, it would’ve been ruined in about a year.
Oh... I think I can do the heat transfer equations. I AM a cook, after all, raised in a family of plumbers.
I had the same issue so I quit taking baths in winter. Water coming out of the faucet right now is about 90F.
There are times you can stand up and yell: IT'S GOOD TO SINGLE!
/johnny