Usually if I get close enough to insert the thermometer I just go ahead and shoot him.
I hear the same thing all the time, but not a phrase that I use. Trying to figure out ones mood or temperature is fairly easy, it's also fairly easy to misinterpret. I've been with people listening to a gobbler who is raising cane, gobbling every twenty seconds or so. They would tell me he's hot and ready to die. I'm thinking no, he's aggravated at those crows he keeps gobbling at. Now if you hear one gobbling a lot apparently on his own, then I'd say yes, he might be hot and might be a candidate.
If your calling to a gobbler and he answers and cuts you off then you might be on to something, but more testing is needed. If you call and he answers once or twice then you have your work cut out for you, but again more testing is needed. If he gobbles once, then again but closer, and again even closer then your on a hot bird. If he gobbles at all your calling and even when you don't call but is walking away then I consider him a lost cause, at least from your current position.
Basically a lot comes into play as far as what his temperature or mood is. Just because a bird gobbles a lot doesn't mean he's hot and ready to die or visa-versa. Some hot birds don't even gobble, those can be tricky.