It is an excellent indication of thyroid activity when there are no complicating factors such as you having a fever. This is why it is used as a quick, cheap measure.
If the temp drops, it mean you have cut your metabolic rate by restricting calories too much. Bumping them up a bit and perhaps even eating a little more carbohydrate will usually take care of the problem.
If you are adjusting your diet downwards or upwards, don’t be too drastic. You may also consider cycling calories up and down within a few hundred to several hundred kcal per day to prevent the metabolic downregulation. These calorie levels should be based on the calorie level at which your temperate drops with at least some of the days having intake above that level.
In general finding a constant intake that allows you to keep temperature up will allow your body to run better and you can watch your skinfolds to see if the results are inline with expectation.
Regardless of the diet you may be on, it is essential that a vast majority (90-95%) of your caloric intake comes from real food (and yes high quality supplements like Metabolic Drive and fish oil are part of this category when consumed in meals that provide a nutrient distribution similar to whole unprocessed foods), otherwise you have other factors that get in the way of your body’s chemistry especially with respect to signaling of the thyroid.
It is much easier to tell people to watch their morning temperature and have intake adjusted based on that than to do more expensive and invasive tests. A higher temperature may be due to sickness or an elevated metabolic rate due to exercise recovery and sufficient nutrients.
Simply checking to see how the person feels can usually rule out sickness, making this an extremely effective and cheap indirect method to get the same conclusion as supported by laboratory test results. That said, this is not a replacement for a full blood panel in diagnosing illness. It applies only to otherwise healthy individuals.