I think the answer might depend on where your thyroid levels are.

I had my gland removed in June of 2011, and everything went fine for the first 7 or so months, then I hit a brick wall and went hypo. Loss of stamina and a ton of random inflammatory episodes. The latter of which were chalked up to "injury" but I never really bought it. Before the thryoidectomy I did half century bike rides, ran 5Ks and successfully maintained a 135 pound weight loss. For two years my endo did nothing but raise my synthetic thyroid medication and it never helped. I switched endos and for the last 6 weeks I've been on natural dessicated hormone (Armour) and things are finally looking up.

However, at the same time I also resumed calcium supplements and added an enzyme called Wobenzym N to my daily regime. So I'm not entirely sure what's working. When was the last time you had a full thyroid panel? That might give you the best insight as to what's going on.

You might also check on your vit D and ferritin levels. Low levels of either can make you feel exhausted as well.

Before I got on a thyroid hormone supplement from my naturopath, I would get so wiped out from exercising. I've been exercising for years and I just kept reducing the amount I could do. My legs were shaky after a quick cardio workout that previously would have been nothing for me. When I got on my current thyroid meds, I started increasing my fitness level again. It made a huge difference. I had been taking a descicated thyroid that I bought without a perscription, but it still had the hormones. It did not work as well. My current meds are without prescription also, but I think you can only get them through a naturopath. It has made a huge difference.

In that book - Stop the Thyroid Maddness - the author talks about being completely exhausted after any exercise before she got on thyroid meds.