It's baseball talk during the off season (winter). Devoted fans never stop talking about the sport, so they stand over a "hot stove" during the winter discussing transactions, managers, anything baseball related.
Term used to describe a person who you are tempted to hook up with despite all logic and reasoning pointing to it being a poor decision. The term draws its origin to when you tell young children not to touch a hot stove but they do anyway and burn their hand. Examples include friend's sisters/brothers, co-workers/bosses, neighbors, roommates, family friend, friend's ex's, etc.
Jeff's crazy sister is a total hot stove to me. She's so hot but I know if we hooked up that it would result in a lifetime of drama.