Answer

The water was not cooked by him, because it had already been cooked beforehand. One could only discuss the issue of a Sabbath violation as it relates to the water at the later time, when it was supposed to have become cold. But even here there is certainly room to be lenient for several reasons: first, he is also the one who turned it off. Second, the water only remained hot and did not become hot because of him, so there is no noticeable prohibited Sabbath result here. In short, in my opinion there is no prohibition.