What is your temperature running at? What did the endocrinologist say about your thyroid and how it's functioning? Did they have any thing to say about the elevated temperature?
That would probably be my starting point. Did blood work show elevated white blood cells like you're fighting some infection in the background?
As for getting sick all the time, any changes in your home? Any mold issues? New schools? New stresses? Is getting the flu-shot a new thing for you guys? That can cause some extreme stress to the immune system for some people (my body reacted with prolonged and extreme inflammation to several major organs after receiving certain vaccines as a teen).
Start at any of those that seems the most obvious, any changes and follow the rabbit trail.
Also focusing on nutrition can really help, upping vitamin C, D3 and K2 in the months of being indoors more due to extreme temperatures.