Shutting off a hot water tap on Shabbos

It’s Shabbos and I notice a hot water tap is on. May I shut it off on Shabbos?

You can turn it off with a Shinuy. (Not the normal way to turn off a faucet. For example you can use the back of your hand to turn it off)

what’s the issue with shutting it off? why does that require shinuy?

Turning off the water makes the cold water heat up faster

Why wouldn’t that be a grams bealma

That’s valid point. But then again turning on the water is the same. The Rav didn’t permit it. (At least when I asked him)