To say that a fight "raged hot and heavy" is quite poetic language. So it is not a common expression, but the meaning is a fierce fight. "To rage" means to be angry, in an active way - shouting about how angry you are, for instance. However, it is poetically used to describe things other than people. Storms and fires are often described as "raging" when they are very violent. So the author is sort of comparing the fight to a fierce storm of fire.