My body temperature ran hot the entire time of my five years of daily hangovers and nightly drinking. I was always hot and sweaty. Sometimes I was cold and sweaty. Other times it switched back and forth between hot and cold pretty quickly.
After a few months of sobriety my body temperature has normalized. I didn't even own a thermometer during my drinking. However, when I did have to visit the doctor my temperature was always normal, even though I felt like I was burning up almost all the time.