The answer is EASY.
Yes, it's that simple.
It's a trap specifically made for people who's very smart like Haku who would read too much into it.
Eventually Haku's 'dumber' follower (the Werecat/Warcat girl) suggest that answer and got it right.
....Behind that door is just "Under Construction" sign and a deadend. (in fact it's not even a real trap, she could've just battered the door down from the go)
Kehma actually hid the temp-core under one of the pitfall traps in the first floor, which he knew Haku would avoid triggering + don't bother to check what's down there properly.