I am on the same page as Sophie. My TB is not a hot one, but he can be, I often find that a few gallops a week keep him happier and more willing to work for me. He just LOVES to run, it's what he is bred for, so, I let him. However, he does have to be well minded during our rides, I don't tolerate bucking or kicking out during the ride, if he gets excited when we gallop generally you can feel it building in his back, at which point I ask for the next gear...He loves it, I enjoy it...but as much as everyone will be chagrined to know, I do use a fairly decent bit, I need to know that should an emergency arrive, that I can stop him. You need to watch though, a TB will run its heart out for you, but then again, that's why I love them.
Sorry I didn't mean for this to be so long :-/