Pinhead is a metaphysical being. When he comes onto our plane of existence, he has to adhere to certain dictates in order to hand out some major pain to his vicitms, this would include becoming part of the physical. He can only be summoned through the Lamentation Configuration Box and as such, is sort of limited on how mobile he can be.
The Thing is an extraterrestrial being(s) that through a single cell can perfectly imitate any physical lifeform it comes in contact with. Remember what i said about Pinhead and his visiting our world. The Thing would have no reason to want anything from Hell it couldn't achieve itself through world domination, so the Box would not be a factor, yet something would have to open it The Thing could have one of it's imitations do this and from there, systematically rip into the Cenobite and imitate him! How are you going to defeat something that even through the slightest contact would be into your system like a sexually transmitted disease with a 100% fatality factor?
The Thing, like I said would be the one handing the beat down instead of Pinhead and his penchant for tearing souls apart. The thing doesn't have one.