At first sight hypothyroidism is a fairly straightforward problem from the aeromedical point of view. It's caused by a deficiency of thyroid hormone (aka THYROXINE) which can be easily replaced in convenient tablet form. It's unlike type 1 diabetes which is also caused by a hormone deficiency (insulin) but whose treatment needs to be given by injections, and which, if not treated almost perfectly, can cause severe effects in several different body organs.
This is the CAA's information sheet on thyroid disorders ( both hypo- and hyper- )
http://www.caa.co.uk/docs/2499/GM%20...ysfunction.pdf
It's interesting that Hashimoto's is not specifically mentioned in that fact sheet. I suspect that the CAA folk might be just a little bit more cautious about the eponymous condition, if only because it's auto-immune, and probably includes an inflammatory component. However, with sufficient specialist reports, and once the condition is deemed stabilised, a flying medical certificate should be possible ( probably even a class 1, though that might have an OML on it for a while).
Good luck !
