If you mindread Ragnar before entering the temple of doom, the key for the top door in that room can be found on the left horn of the dragon statue (walk forward until you get to the first wooden plank, turn right and look down). There is not much in there, though, just Jagon's diary and some lowish level random loot.
In the area with the lava I tried for the first chest a few times, but the best thing I got was a healing potion, which I needed to use to make it back out alive. The chest at the far end is easier to get to, and I found a half decent formula with a couple attempts.