It was no ordinary volcano
When Sauron began searching Middle-earth during the Second Age for a permanent dwelling place, his attention was immediately drawn to Mordor, and especially to Orodruin, whose power he believed he could use to his advantage. He subsequently established his kingdom based around Orodruin and "used the fire that welled there from the heart of the earth in his sorceries and his forging". The most famous of Sauron's creations forged at Mount Doom is the One Ring. In The Fellowship of the Ring, Gandalf explains that the materials of which the Ring is made are so durable and the enchantments with which it is imbued so powerful that it can only be destroyed in the Cracks of Doom where it was made.
Orodruin is more than just an ordinary volcano; it responds to Sauron's commands and his presence¹, lapsing into dormancy when he is away from Mordor and becoming active again when he returns. When Sauron is defeated at the end of the Third Age, the volcano erupts violently.
This is implied evidence from two observations
Sauron extended his own power into it, and was able to control its fires. It seems to have lain dormant when Sauron was away from Mordor, and sprung into life when his power grew. After the Downfall of Númenor, for example, the Exiles in Middle-earth first knew that Sauron had also escaped the Downfall when they saw smoke rising from Orodruin, and an Age later at the Council of Elrond (The Lord of the Rings II 2), Boromir says 'The Nameless Enemy has arisen again. Smoke rises once more from Orodruin that we call Mount Doom'.
These two infer that when people saw activity from the volcano, it implied the Dark Lord was up to machinations at The Fire Mountain. The suggestion is that somehow his powerful magics were activating the volcano, i.e. causing it to respond.
Side remark:
It isn't clear how Elrond or Círdan could know that throwing the Ring into Orodruin would destroy it - neither of them had had any part in the making of the Rings of Power, and both had refused Sauron's lore when he offered it to them. At this time, though, both Elrond and Círdan were themselves Ring-bearers (of the Elven-rings Vilya and Narya), and perhaps these Rings gave them special insight².