I'd say purty hot. About as hot as the air temp inside of it. I'd think if you kept a clearance gap you'll be OK. Even a fireplace flu only requires inches of space for code. Also, I doubt the drum's ever going to get so hot that the lumber will combust.
18.5", 22.5" OTS
Large BGE (chambersuac's)
The Fiery Furnace (chambersuac's)
Big JT's Smokin' BBQ Competition Team