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Because

the door handle was still hot from the furnace test, so it was a trap room
He slowly removed his hand before triggering the trap
He went to the next door (now a 1 in 3 chance), opened it, did not smell acid or see bullets on the floor, so he went in. Had he smelled acid or seen bullets, he would not have gone in (and not have gotten the treasure).

Because

He first examined all of the doors. He was able to see damage to two of them from bullets and acid respectively, so those two were trap rooms

When he touched the door handle of one of the remaining two doors, it was still hot from the furnace test, so it was a trap room  

He slowly removed his hand before triggering the trap  

He went to the last door and opened it and he went in.

Because

the door was still hot from the furnace test, so it was a trap room
He went to the next door (now a 1 in 3 chance), opened it, did not smell acid or see bullets on the floor, so he went in.

Because

the door handle was still hot from the furnace test, so it was a trap room
He slowly removed his hand before triggering the trap
He went to the next door (now a 1 in 3 chance), opened it, did not smell acid or see bullets on the floor, so he went in. Had he smelled acid or seen bullets, he would not have gone in (and not have gotten the treasure).

Because

the door was still hot from the furnace test, so it was a trap room

Because

the door was still hot from the furnace test, so it was a trap room
He went to the next door (now a 1 in 3 chance), opened it, did not smell acid or see bullets on the floor, so he went in.