The saliva cortisol its the most accurate, yes. Checking ACTH would be helpful. The low body temp can be linked to hypothyrodism which I have and its usually involved with AF.
The standard tests for endocrinology (and most other areas) that the ridiculous, greedy and foul smelling doctors will make you will come always "within the normal range or slightly low or high, nothing to worry about take this antidepressant and f*** you, have a nice day poor suc***".