The One Ring was forged by Sauron in the fires of Mount Doom itself - probably at the very spot that Frodo and Sam (and Gollum) were standing in, above the fiery pit. Thus, I think it's safe to say that the destruction of the ring isn't linked to a specific temperature or melting point, or even to some mystic energy left over from Melkor's spiteful attempts to mar Arda, but to a much simpler case of closing a circle - where it was forged, there it shall be undone. It's a symmetrical correspondence that works well both on a thematic/narrative level, and also on a metaphysical/mystical level.
Of course, this does leave us with Gandalf's (Or was it Elrond's?) comment about dragonfire destroying Rings of Power, but I think that this is mostly speculation, and idle speculation, at that, even by Gandalf's reckoning - he noted both that the ancient dragons are long gone, and that even if they were, the One Ring itself would probably be too powerful even for them to destroy. Gandalf knows that it's Mount Doom or Bust, but allows himself the brief luxury of remembering Ancalagon the Black as the lesser evil.