Why would a child have a low body temperature?

May be hypothyroid. If you are not very ill, which can lead to a low temperature, and the temp is below 97. 6, you may be hypothyroid. Remember, 98.6 is average, normal can be 1 degree above or below. The temperature normally goes down at night and is lowest about 4:00-6:00 A.M. About 2 hours before awakening. Then it can be as low as 97.