I know nothing about the subject, but got curious and found
this article on Google Scholar, a copy/paste from some journal. It's conclusion:
In conclusion then AAS seem to have little if any effect on thyroid function per se. The reports by Deyssig & Weissel, and Daly et al suggest the possibility of a direct action of AAS on the thyroid or pituitary, but their results are inconsistent: The former researchers detected elevated stimulated TSH while the latter saw an increase in basal TSH. Free T4 was unchanged in former group, while it was elevated in the latter. The only consistently reported effect is a depression in total T4, total T3 and TBG. If there is a direct effect of AAS on the thyroid, pituitary, or hypothalamus the studies conducted so far shed little light on the mechanism due to their inconsistent results. And as stressed by Deyssig & Weissel any direct effect of anabolic steroids on the thyroid would likely be of no clinical significance due to its small magnitude.
From a practical standpoint for those concerned that anabolic steroids might suppress the thyroid it is a simple matter to incorporate low dose (25 to 50 mcg/day) T3 into a cycle to enhance fat loss while at the same time only minimally if it all compromising gains in muscle mass (10). In (10) one group of subjects was given T3 alone while the other was given a combination of T3 and testosterone enanthate, 200 mg/week. After 28 days of bed rest, the men in the T3 group lost an average of 3.9 kg of body weight (i.e. from 82.0 ± 7.1 to 78.1 ± 7.1 kg). Body weight in the T3 plus testosterone-treated subjects declined by only 1.0 kg (78.9 ± 4.9 to 77.9 ± 4.9 kg). Lean body mass declined by 1.5 kg in the T3 group, whereas the T3 plus testosterone-treated subjects experienced nearly a 2-kg increase in lean mass (i.e. 1.7 ± 0.9 kg). Of course we don’t know how much mass the test plus T3 group would have gained had they foregone the T3. Nevertheless these are still impressive gains considering the subjects were forced to lie in bed for 28 days with no exercise, and considering that no special dietary measures were imposed to preserve or increase muscle mass.
(10) Zachwieja JJ, Smith SR, Lovejoy JC, Rood JC, Windhauser MM, Bray GA. Testosterone administration preserves protein balance but not muscle strength during 28 days of bed rest. J Clin Endocrinol Metab. 1999 Jan;84(1):207-12.
