Do you run cold or feel cold? Because those are opposite. If you run hot, temperatures should feel relatively chilly. Like when you run a fever you feel cold.
Fever is the immune system fighting infection. The better comparison is to light exercise which increases temperature and perceived temperature. Perceived internal temperature is in general most closely related to movement.
Feeling cold and having a low body temperature are not equivalent. Take your temperature as soon as you wake up for a week to know your normal resting temperature.