The two words together don’t seem intuitively to result in a meaning that an election or a race has resulted in a tie. Word Wizard says the expression was first used in horse racing. Dead “…means absolute…complete, from the idea of finality of death.” Heat can mean “…a single course or division of a race.” From the fourteenth century heat was taken to mean a “…a single intense effort or bout of action” and the “…single run of a race.” From that explanation, the two words together meaning that something resulted in a virtual tie makes more sense.