I have the same heat intolance problem you do but since got off meds against doc advice, screw them, it is not as bad.
I take a multi vitamine, l-tyrosine for feeling good and it helps for the most part.
I go see my alternative/internal doc again on Tuesday and will ask to get progestrone cream as she suggested in the past and I never did fill the prescription.
She actually listens to me and my symptoms and suggested maybe it's adrenal gland problem.
Sometimes the fillers in the meds change and it can cause' problem. I didn't have too much of a problem in the begining on levoxl and syntroid but later on it became unbareable so I said screw that and went off cold turky very hard withran symptoms. I know I need something but not sure yet.
The key is to find a good doc who has experiance with the specific you have and that actually listens and is willing to give you not just pharmcuidacal but vitaminine/mineral and alternative.
I am Hypo and not Hyper so I don't know too much about your medication for Thyroid, although I was on Metoprolol for over a year, I always had chest tightness and pain to the point I thought I had heart trouble, I had a fast heart rate and moderate high blood pressure at the time the Cardiac md put me on 100mg Metoprolol, He did not know at that time that I had Hashimoto's and that high Bp's and fast heart rates are part of the package with thyroid disorders, I did some checking into the side effects of Metoprolol, It seems that it affects the muscle valve(Spincter) that is located at the bottom of the esophagus, where it enters the stomache to relax and stay open, this in turn allows stomache acid and acid fumes to flow up into the esophagus and cause severe (Acid Reflux) tightness and pain in the center of the chest from the breast bone and above, After being taken off of Metoprolol and put on a different Blood Pressure Med, the chest pain and reflux went away.
Have you had a Ultrasound to determine if your thyroid is inflamed? I was told my thyroid is 2.5 times larger than it should be at the time I was diagnosed, I had trouble swallowing, hoarse voice, and all the other symptoms until my Labs came out in the ball park and I reached the right Free T3 level. Good Luck FTB4