Does turning off a hot water heater before Shabbos make it permissible to use the hot water from the sink on Shabbos?
Not necessarily. If the water in the tank is still “yad soledes” [over 110 degrees], there are still 2 concerns. If the hot and cold water are turned on at the same time, the hot water may cook the cold water. This could be avoided by only turning on each one by itself. In addition every time hot water is released from the tank, new cold water enters, This may be cooked by the hot water in the tank. To prevent this the water input needs to be turned off. If these concerns are dealt with the hot water may be used for permissible purposes on Shabbos.