i've tried running thru, that didnt work either. what i do is go down the stairs, go thru fire, walk back thru.. then go along the edges, but soon as i step close to the gate, it comes flying down, and then i cant get out ugh.. maybe i'm just not cut out to be a explorer.. lol, if i was really in this group, i'd have one undo the trap, while the other was at the door, then move a crate in the doorway, so the others could come thru.. too bad i cant split up my party!
TJ

Have your "leader" carry a crate and go through the fires as quickly as possible. The crate should block the gate coming down which should then allow your characters to get out. That's how I did it on two separate games. Hope you figure it out!
Wyv

You have to avoid the middle fire (the one that heals). If you touch this fire it resets the puzzle.

Have your priest rested and ready to heal your party members. Go through the first fire and stop. Have your priest heal everyone to full and wait for him/her to gain his spells back. Then proceed to the side and flip the switch. Proceed around the edge of the room (stopping to rest and heal after each fire) until you pull the second switch. Never go through the center fire or you will reset the puzzle and have to start over! Be prepared for bats and bandits to pop out at you as well. I used my wizard to blast them quickly. Have fun!

The real way to do the puzzle is to hit both switches without touching the healing flame. I didn't know this at the time and was very resourceful. You can do it their way with the crate, but thats trouble too. I got off to either the left or the right of the door, around the corner. I was near the flame but forget if I had to get in it or not but if you do just heal with the heal flame. You can try to come around the corner pretty fast without looking at the door and theres a good chance that you'll slip through. its a tricky thing as you don't want to go square around the corner. The distance around the corner that opens the door is much less than directly away from it. I didn't even know how to run at this point (you run by holding shift) and I did it twice pretty easily.
You will get hurt by some crush damage from the metal gate closing so heal once through the gate since their are some specters up ahead to fight.