The thyroid is a tricky gland, and the hormonal replacement of thyroid hormone is also tricky.
Bits and Pieces:
From discussions about panhypopituitarism, there are a significant number of folks who prefer the Armour thyroid preparation instead of levothyroxine, and feel better on it. Endocrinologists seem divided on which they prefer.
There are a few folks I know who regularly use anabolic steroids, and they've told me that taking T-3 is the difference between an mediocre cycle and a very productive cycle, given the other variables remain the same. They all, after regularly supplementing their cycles with 150-200 mcg of T-3 on a daily basis, for over 8 weeks, have a fully functional thyroid (after the HPTA rebound occurred)
I do not think you can look at body temperature upon rising, in a healthy individual, and comment upon there thyroid output without a hormonal make-up before hand. A few years back I had some thyroid test done (my doctor wanted to check the levels so he could prescribe me some drugs if I was deficient...didn't matter what drugs, but he was hoping for statins, diuretics, and maybe thyroid too) and I followed a similar procedure to chart my temp...borderline low, but my thyroid output was fine.
I do not think that IF is going to affect the hormonal axes more than CR might, CR is, by far, a much more dramatic intervention in the energy balance of an organism.