unless the ring is destroyed.

I guess the temperature generated by a thermonuclear device should by far exceed that of the fires of Mt. Doom. So with conventional physics, the ring should be destroyed. With magic getting in the way, the destructibility of the ring could be directly linked to the actual fires of Mt. Doom, though. Anyway, one of the more unhinged noncredible contraptions dear old Dr. Strangelove Edward Teller dreamed up could destroy all of Middle Earth, which would sufficiently diminish the power of Sauron through the extinction of all species susceptible to the ring's control, even if the Ring stayed intact, and he survived. This would surely piss him off big time, and therefore be very funny.