Welcome to the forum, We love pics here!! Please feel free to share you're pony pics
As for your question. There are SO many places to start with this. Yes TBs are hotter than average horses, but there are many factors that add to heat.
What is her daily schedule?
How much turn out and other exercise has she got?
How much time cooped up in a stall?
What is she getting as far as feed (please be real specific- weights and brands)
How long have you had her - how old is she?
What was her previous life - did she race?
My next BIG thought is pain - bucking under saddle usually to me SCREAMS pain issue. Have you had her thoroughly checked by a vet, dentist, chiropractor? Saddle fitter? Is pain 100% ruled out?
I'm happy to help more just think there are too many possible explanations to really dig into one route.