There are two doors in that cave that need keys to open. The first 'Fire key' can be founded behind the magical wall to the north what can be turned off by flipping a switch on a wall on the south part of the caves. That key unlocks the door near the switch you flipped. There can be found the second 'Worn Fire key'. (after you solved a puzzle-kind thing
) And this key opens the gate to the east, and that's the finish. Good luck!