남아돌다 means "superabound; to be very abundant or too abundant" 남아도는 means "being a surplus; being in excess of what is required" 남아도는 열기 means "a surplus of heat"

남아도는 simply means "to be in excessive of something". In this sentence, it kinda translates to "When the physical temperature of your body increases, the excessive heat is released in a form of sweat through the skin." 남아도는 열기를 (excessive heat) 피부 밖으로 내보내기 위해 (in order to be released through the skin) 땀이 나다 (sweat forms) Native koreans, correct me if I'm wrong please. Haha!