This is a lot worse than fudging a roll when you really don't want your character to die. (and that's pretty bad.)
Boot the guy. He not only ruined it for himself, he ruined it for everybody else.
That's absurd.
However, like BardStephenFox said... make sure that you're not running a DM vs players game. I think it's a little bit off the mark, though... even if you are, the guy shouldn't be cheating, he should be telling you what he doesn't like.
But, in any case, yeah. If you don't want to boot the guy, tell the guy you'll boot him if anything like this happens again. If it does, do it. If you've already talked about this, follow through and boot him. That's the "easy" way, and the way I'd follow if the guy was my friend.
If the guy wasn't my friend, I'd hope to never see him again. Simple enough!
As for the other players, well, they're still somewhat at fault... anyway, as above posters said, if you still want to run the dungeon, just start mixing things up -- and if anybody does suspect things like "i go search the bed" ... well, spring a trap or an ambush on them. If they get offended, well... good.
It's usually good to mix things up a bit in a module anyway, if you have the time to do it and do it right. I wager, at least.
anyway. g'luck w/ the crummy situation, I hope you find a good way to work it out.