I will not attempt a halachic opinion. But I will mention that we sometimes turn off the “breaker” on our electic panel – the one that is for the hot water heater only.
The water is then warmish, depending on the season winter or summer and can be used for washing hands or dishes more pleasantly than the icy water from the cold water faucet in the winter.
Some might say the warm is very hot Friday night and might be a cooking question as well, when water enters the tank. If many take showers close to Shabbos, this will make the water only lukewarm when Shabbos starts.