I think I have begun to understand what is wrong with me.
My low body temps are due to high cortisol causing poor quality sleep and then the poor quality sleep causes an underactive thyroid.
When I sleep well, usually after sex, I don't get low body temps and feel almost normal. Testing shows normal TSH when I am well rested and a high TSH of nearly 7 when I am sleep deprived.
People with adrenal fatigue also suffer copper overload. I haven't attempted a copper detox yet, I've ordered some taurine (thanks Laredo7 for the advice!) before I start to detox with zinc and molybdenum.