Thermoregulatory Dysfunction and Parkinson's

We (my husband who has PD and I) are learning that every person experiences different symptoms of Parkinson's and we are wondering if others experience Thermoregulatory Dysfunction. My husband has feelings of sunburn on his temples, cheeks and forehead and groin and his arms, legs and hands are ice cold to touch. This is constant - he has no 'regular' body temperature. It's so severe it's hard to enjoy anything. His doctor said to were gloves !!!! Surely there is something more that can be done to help regulate body temperature. Thanks for any experiences others have had that may help.