Low temperatue is a hallmark of hypothyroidsim, as are all the symptoms you've described. Lupis and thyroid disease can often go together (as most thyroid disease is autoimmune too). You need some good labs to see if this is the case with you. Here are the ones to check.
TPO and TG antibodies
Post your results here with the lab ranges even if you fall within range and your doc tells you your thyroid is fine. Most docs aren't too good at interpreting these labs.