What should one do who doubts having had a wet dream upon waking, then Satan tempts him as the day progresses?

The best cure for obsessive thoughts (waswasa) is to ignore them, along with frequent supplication and asking Allah for well-being. The basic principle is that a person remains in a state of purity, so he is not required to perform ghusl (ritual bath) unless he is certain that he has become impure (junub), even if he strongly suspects it. The Prophet, peace and blessings be upon him, was asked about a man who imagined he felt something during prayer, and he said: "He should not leave until he hears a sound or perceives a smell."