I had my Bose Bluetooth speaker playing in the kitchen the other day, with my phone in my pocket. As I walked towards the front door, the music stopped. Walked back towards the kitchen, and I heard the speaker re-link to the phone and start playing music again.
Point being, this was through 3 rooms that have a clear line of sight. No walls in the way. Would I trust a Bluetooth thermometer that's outside on the smoker to be able to communicate with my phone? Nope. If it were wifi, I'd buy into it, but the range on Bluetooth isn't far enough.