The pontiffs of Chouli Mutt - Jagannath Swami (21), Sharanayya Swami (18) and V Reddy Swami (50) - allegedly set fire to a place where firewood was stored in the mutt complex and jumped into the fire, they said.
Fire brigade and police personnel recovered the charred bodies from the spot. Police said the trio had left a suicide note, which was being probed.
Chouli Mutt seer Ganeshananda Swami had died under mysterious circumstances in February, they said, adding that his three juniors were reportedly upset about it.
The mutt, which attracts followers from the Lingayat community, has been dogged by controversies over property related issues.