I have really low body temperature myself , it goes down to 95.5 on occasion but generally to 96.2 to 97.5. I also have hard time gaining weight and I lost weight in the last years I am presently stable at 152 5"11.
The main thing with body temperature is that if there is big variations during the day and your temp are not stable adrenal are usually the issue and taking thyroid med will be hard on the adrenal and the whole body.
You should usually always support the adrenal first and then the thyroid if it does not clear up by itself.
Check this out it will guide you.
weight loss is also generally an adrenal symptoms check on the dr rind symptoms matrix under temperature pattern.
Right now I am supporting the adrenal big time with beepolen , panthetine , acerola , nettle, SJW and will be adding licorice and adaptogenic soon. If this is not enough (will see in one month or 2) I will go to another treatment option , maybe pregnenolone and then ultimately hydrocortisol. Hopefully I get some good result with what I am taking now.
I have some encouraging result with the supplement and cannot wait to had the licorice and adaptogenic aswaganda but nothing close to a breaktrought yet were I could feel like I am near my old self.
Keep us posted on your result and treatment and do not fly away when you get better : TELL US WHAT YOU DID !!!