To be fair, I do not use MDMA often- since I've been on thyroid treatment, I have used only 3 times.
I have a couple of friends who are MD's who I can openly ask about my drug use conflicting with prescriptions, and though I don't always think being a doctor means they truly know the answer, they both don't feel they pose any conflict.
I have done bk-MDMA about 4 times while on thyroid treatment, with no noticeable different in the experience either. I'd research as much as possible to see if there is any actual data out there. Don't bother with Yahoo Answers unless you just want to laugh.
Is you concern coming from the fact that a symptom of underactive thyroid (hypothyroidism, Hashimoto's etc.) is consistently being cold, and therefore the synthetic thyroid medication would balance that out and make your friend have a higher potential for over-heating? I can tell you though I personally have a "balanced" thyroid from my meds, I still suffer from being constantly cold, having energy dips, and always always being hungry (more related to an excess of ghrelin, which is common for people with underactive thyroid)- but taking the medication has balanced out my thyroid, which is most important.
In terms of doses, I tend to go big and re-dose. I don't do MDMA often, but when I do, I'm rather intense with the dosing, admittedly. I am one person, and you should not base your decision on just my circumstances. You may likely get a lot of negative answers if you check out the popular thyroid message boards, but you may actually get some helpful ones too.