Was the Balrog drawn by the ring?

[Alfirin]

For most other flying things, one could argue that it may be only capable of soaring/gliding (or only has the strength to get up in the air and then has to rely of soaring to stay up, like many birds) and the cave has no thermals to ride. But for a Balrog even that would not make sense. Since they produce fire (and unlike dragons, that fire seems to come from their whole bodies/the weapons they carry; not just their mouths) they'd basically make their OWN thermals.