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:

From splendour he fell through arrogance to contempt for all things save himself, a spirit wasteful and pitiless. Understanding he turned to subtlety in perverting to his own will all that he would use, until he became a liar without shame. He began with the desire of Light, but when he could not possess it for himself alone, he descended through fire and wrath into a great burning, down into Darkness. And darkness he used most in his evil works upon Arda, and filled it with fear for all living things.

And in "Of the beginning of days":

And in the darkness Melkor dwelt, and still often walked abroad, in many shapes of power and fear, and he wielded cold and fire, from the tops of the mountains to the deep furnaces that are beneath them; and whatsoever was cruel or violent or deadly in those days is laid to his charge.

Volcanoes are explicitly associated with Melkor in the Silmarillion as the remaining scars on the world after the Valar "repaired" the damage:

In that time the Valar brought order to the seas and the lands and the mountains, and Yavanna planted at last the seeds that she had long devised. And since, when the fires were subdued or buried beneath the primeval hills, there was need of light, Aulë at the prayer of Yavanna wrought two mighty lamps for the lighting of the Middle-earth which he had built amid the encircling seas.

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:

The lands of the far north were all made desolate in those days; for there Utumno was delved exceeding deep, and its pits were filled with fires and with great hosts of the servants of Melkor.

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.