When you feel your body is on fire, do you sweat? Sweating would provide cooling and if you had trouble sweating (which can be a disorder), your body temperature could rise and cause a fever-like condition.
When I exercise, there is a point where I reach a state physically during the workout where I get a boost of energy. It's like reaching the top of a hill and coasting downhill. But, it's not the fiery energy you describe. That is interesting.