Hi Carly, what are you training your horse for? Is he turned out into the pasture, and if so are there any problems there?
When he stamps his foot is he in cross-ties? If so he may think that he is in a starting stall waiting to burst into action.
Does he do the stomping before riding/training, after, or both? Does having his saddle on or off make a difference?
What are you feeding him and how much are you feeding him? TBs are often a lot more sensitive to lots of concentrates than a lot of breeds and it comes out in their behavior.
You might want to consider looking into getting a clicker, this way you can show him exactly what you find acceptable, by clicking and rewarding him during those brief moments he stands still.
Sorry I can't help more, the only time I had this problem was when I boarded an Arab colt of mine and his feed was changed to a super-charged feed high protein feed and he was jumping out of his skin. Changing him back to regular 10% protein sweet feed made all the difference in quieting him down and he stayed quiet though he was still a stallion.