Dying in the Heat is about getting caught up in the routine of a relationship. In this case, the narrator feels as though they are giving and sacrificing a lot more for the sake of the relationship to make it last and getting nothing in return. They’re overexerting and therefore burning out or “dying in the heat” of this love affair.
It’s about how much people will give just to remain in their comfortable routine of a relationship even though it may not be worth it in the end and leaving for someone who will appreciate and value them more might be the better option. That’s symbolized by the “storming coming” at the end of the song when the narrator has had enough, claiming they “never want to fall in love” (again).