The temprature has to be taken before you get out of bed and make sure you do not move too much. Slight movement raises your temperature.
You are right about other times when temperature goes down are, when you are fasting on water, exposure to extremely cold weather, for women during their periods etc. But this is different basal temperature taken when waking up is an indication that you have some thyroid issue.
Please go on Iodine forum and read the past posts.
I am only telling you what I have learned from experience.