My best guess is the thyroid dose is the culprit here and that it set off a chain of events that increased your latent anxiety, which explains why it lasted after decreased dose, although I am not sure how long that has been from your narrative. Thyroid often masquerades as anxiety and since it causes similar symptoms you become hyperaware of your body, more self observant, and lose your perspective. Now you are afraid it is ms, another anxiety that is almost certainly now grounded in reality.
Thyroid may cause such problems, but you don't seem to be hypo or hyperthryoidism, since your t3, and t4 were normal.
Now another gland can affect the thyroid, and give similar symptoms, and that would be the hypothalemus, which can affect thyroid too. You may have a low cortisol count, which directly affects the hypothalemus. Very few things can change your tolerance to heat/cold, etc. Your thyroid may not even be the culprit if your cortisol levels are low. You should do a follow up and see if they tested your cortisol levels, usually a blood test is done, but is a poor means. 24-hour urine test for cortisol levels is the best way.
AND YES stress CAN be the culprit, regardless of what some may say otherwise:) Although it's usually just a fuel for the flame. I had similar problems after abrubtly stopping WellButrin XL, I'd take it some days, some days not, off and on. I am now at the point where I can't even walk for more than 10 meters without developing symptoms of hyperthermia. House tempeture is at 68, and I still sweat when I move around. It got so bad I felt like killing myself, the constant nausea and pain was not bearable. Fianlly we found out Wellbutrin was the culprit, or so we think, lol.
Anyway stress can affect people in ways worse than they can imagine. I was prescribe valium, and I suppose it calms me down enough to where I can kind of sit in my chair without feeling too sick, walking still kills me:) So valium may be of great wonderful help. You may need a higher does than the standard 5mg, if the stress is that bad. I had to take 15mg(3 pills) to even notice an effect. Also I never felt drowsy, and this is WITH a muscle relaxer (Dycyclomine) (SP) Valium is used mainly for stress, and may help with these types of problems if your readings are pretty normal. Be sure you're eating enough, as anemia may make it worse.
If it does have something to do with low cortisol level, percodan is a nice mix of stress relief, pain killer, and has caffeine which would raise your cortisol levels. Paxil would work even better, for stress, and it can increase cortisol by as much as 700%. DR's who specialize in your problesm specifically are called endocrinologists, you'll get a much better answers and help with an endocrinologist. They specialize in hormonal problems, thyroid problems, etc, you won't find a better suited professional to help you with this.
Note that your DR. probably sent you to a neuroligist because you mentioned something about MS:) Neuro's specialize in MS too, but don't worry, I doubt he sent you there because he had no more ideas, not that he thougt you may have MS. MS is very very hard to diasgnose, the neuro should be able to help to see if it's MS or something else, since you're already seeing him, if you don't have MS, or if he's not sure....seek an endocrinologist:)
I am no DR. Do not try anything I have said here without consulting your DR. and for the love of GOD see an endocrinologist:)