Was there something more mystical about Mount Doom that meant another volcano wouldn't work and no matter how much energy was put into it, it would not be destroyed? A comment mentioned that not even Ancalagon the Black, the greatest dragon, could not have done it; but how about a Balrog? What about another Maia or a Vala? Could a sufficiently advanced technology destroy it? Given that middle earth was becoming more industrialized wasn't it only a matter of time until a furnace or other artificial heat source that was hot enough was created? If some catastrophe destroyed Middle Earth entirely would the ring be unmade, or would Eru have to do it himself?
A possible explanation from the canon is that volcanoes were remainders of the doings of Melkor (Morgoth) in his attempts to undo the work of the Valar in the "days before the reckoning of time". In the Valaquenta, the Silmarillion says of Melkor:
And in "Of the beginning of days":
Volcanoes are explicitly associated with Melkor in the Silmarillion as the remaining scars on the world after the Valar "repaired" the damage:
I think that Sauron, being Melkor's most powerful disciple, would have forged the Ring in the fires of Utumno, if he would have had the opportunity:
However, Melkor's fortress was utterly destroyed after his downfall. Perhaps Mount Doom still held most residue or echoes of Melkor's power or malevolence.
Mount Doom was where the Ring was forged, so the implication was that only its fires could destroy it.
If any other odd volcano could do it, Gandalf wouldn't need to risk the Ring falling into Sauron's hands by sending Frodo into the middle of Mordor
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I think that physics phenomena such as heat are irrelevant here. The Ring must be destroyed at the end of the Journey, by a combination of Magic and Fate. It is not only the intense heat of Mount Doom that destroys it, but the fact Mount Doom is an important feature of Middle Earth, back from an ageless time when... etc, etc.
A technological terror like the Death Star could not make a dint in the One Ring, merely because said weapon is neither ageless nor magical in nature. [Note: I mention the Death Star because it is what the original question was about, before it got edited].
Now, if one were to use the Force... :P
Supporting statement from Elrond (from the movie, unfortunately):
He never says "... Or any other fire of equivalent intensity".