Just go with room temperature. As a side note, I looooveeeee TBIII. It's just a little more expensive than TBII, but it's waterproof, just as easy to apply, and really strong. I used it to glue on a longbow riser and only realized after tillering that the grip was bending some.
The titebond didn't loosen at all.
DISCLAIMER: Don't glue on bendy handles it will break yadda yadda yadda...