The other option is to directly measure basal metabolic rate while sleeping. That might be easier to do as a home thing these days. Barnes had to get people to go to the testing centre and then be scared stiff by complicated apparatus. They got all panicky and screwed up the test.

But if there's some way of measuring BMR while sleeping in your own bed and you can do it every day for a week until you stop getting nervous, that looks like it would be sound.

Agreed. Some sort of 24-hour continuous thermometer attached while you slept might be good. And ideally you want to measure skin temp and outside temp, since what we're interested in is the amount of heat passing through your surface, not your temperature per se.

But Barnes reckoned axilliary waking temperature was the best test, and he was a proper endocrinologist with access to whatever tests he wanted, and he looked at lots. And everyone thinks he was a loony because he said hypothyroidism was really common and explained everything. And I did too until I realised I'd just predicted the same thing from the simplest explanation for my mystery.