Temperature sensitivity is sometimes seen, but if stable on thyroid meds, would look at other causes as there would not be much more that could be done from thyroid standpoint.
I just noticed your post was for an MD, If you want an MD, Click on Experts Tab at the top of the page, this is a thyroid forum, where you can discuss symptoms, ask questions and gather info. Welcome. FTB4
It is common to be cold with Hashimoto's, since hormones do affect body temps, I have Hashi's and get cold sometimes, I will be cool while others are warm in the same room, My body temps run cooler than normal anywhere from 94.5 to a high of 97.6, but never higher than that. Have you taken your temps?, to see if your body temps are cooler also.
Good Luck FTB4