Our core body temperatures can vary from a high of 100 degrees in the afternoon with lots of activity to a low of 96.1 in the early morning hours before we awaken. So, depending on the time of day, the readings can be persistently "low" normal. (Best time to measure it is 3-4 hours after awakening.)
Historically, the temperature of 98.6 was arbitrarily decided hundred years ago using one german subject. We now know better.
With that said, there are alot of things that can cause low core body temperatrure besides wilson's syndrome. (make sure they checked a T3 level) . In my athletes, the number one cause is due to overtraining, This is due to the vicious cycle of release of a milieu of stress hormones (and your cortisol level is on the high end of normal) .
The elderly have lower than normal core body temperatures due to their decline in melatonin production (which is why they rarely mount a fever when they get sick). Thus, shift workers, or those who have irregular sleep hours or those who expose themselves to alot of light late in the evening will have affected their melatonin production and can have low body temperatures. Mine runs 96 all the time because of this. Those who live in constant abuse (sexual, physical, mental) have lower than normal body temperatures due to the contstant state of stress that they live in. Sometimes this is the only clue and they are confronted with that question with an affirmative answer.
If you are worried about the adrenals the most accurate test is to do a morning cortisol level combined with something called a dexamethasonse suppression test. They are not easy and have to be done exactly right (ie: at 8:00 am before arising...so we do the cortisol level in the hospital while in bed to achieve the most accurate results.)
You have a good differential for low alkphos, but there is one other important one, exogenous male or female hormones, thus, in some steroid users, this is the case.