Question Regarding Child Overheating

We asked our ped. about this too since the girls instantly overheat in any temp. above the 70's or if wearing too many layers of clothing. Our little one can't even sleep with a blanket and our house is pretty icy with the air conditioning on. He also thought it was a lingering effect of a slight case of rickets- vitamin D defiency. So, we work on getting them lots of vitamin D everyday, hydrate them with water, pour water over their heads outside, and really I rarely let them outside between 11:00-4:00 because they are saturated in sweat and red from head to toe within 5 minutes. Just something to look into. Good luck!