Upon entry, use Sly's jump attack to close the furnace doors. Jump on the small metal walkway and collect the clue bottle hanging off of it. Continue on and take out the Welding Walrus. Next, sneak around the pole using the blue stealth auras, then climb up to the upper ledge and do the same thing. You will come across another clue.
Next, walk across the large spinning cog and break open the grating. Head through the ventilation shaft and you'll approach a giant room that has several furnace doors with clue bottles on each one. Collect all of the bottles up here, then drop down and lay waste to the Belly Walrus. Smash the alarm and head through the tube leading into the next room, which is laden with deadly, spinning electric fans that must be avoided at all costs. Walk across the wooden floor, avoiding the propellers, until you come across a pipe. Climb up to the higher platform, then scurry along the pipe that lines the fans. Try your best to avoid these hazardous fans once more. You will then approach another tube entrance.
You will enter another furnace room just like the last one, but this time, there are lasers between each set of furnace doors. Avoid the lasers, collect the clues, then smash the alarm. You will then reach the final room. Walk across the spinning tube and dispatch the Hammer Walrus. Collect the clues on the left. Then, jump off to the left to collect a couple more clues on the pipes. Climb up and head across the black platforms to the other side of the lava, then smash the safes to reveal more clues. One more clue will be seen hanging from the top, near the hook. Head up there and collect it to open the vault. After cracking the code, climb up the gears to reach the top again, then hang on the hook and let it carry you the furnace. With the shaft stopped in place, head through it and shut the furnace doors. Straight ahead is the spinning crankshaft with the treasure key on it. Leap to it carefully and collect the key.