Hot Water on Shabbat

Question

You write: The only problem with turning on the hot water is that you are automatically bringing in new cold water into the burning hot water tank, that is getting cooked instantly. This is like cooking on Shabbat. 125 degrees or less is not hot enough to be considered cooking. Is there not the additional problem that the flame will ignite to raise the temp of the water cooled by the recent intake of cold water?