In the pilot episode of 30 Rock, NBC executive Jack Donaghy (Alec Baldwin) explains the “three kinds of heat” to Liz Lemon (Tina Fey):
The GE trivection oven cooks perfect food five times faster than a conventional oven because it uses three kinds of heat. Thermal technology for consistent temperature, GE precise air convection technology for optimal air circulation, and microwave technology for incredible speed. With three kinds of heat, you can cook a turkey in twenty-two minutes.
The trivection oven is an actual GE product and Jack’s description is taken nearly verbatim from GE’s website. Jack uses the GE trivection oven as a metaphor to explain the changes he is about to bring to TGS, the show-within-a-show of 30 Rock. Jack explains he is adding Tracy Jordan to the cast, who will be the show’s much needed third source of heat.
The “three kinds of heat” is likely a spoof of something Tina Fey heard an executive say, but it’s an accurate description of what is needed in storytelling. If 30 Rock was only about Liz and Jack there would be something missing — two main characters and their interactions (despite their very different personalities and values) would not be enough to sustain the show, nor would they have much reason to interact. The third main character, Tracy Jordan, is the link between Jack and Liz. Without Tracy (who Jack hand-picked to be on TGS) there would be little reason for Liz to constantly interact with an executive like Jack. Tracy pulls these two disparate people together and gives them something to have conflict over. He is the third heat.
As a general rule (and there are of course exceptions, which you will no doubt look for) when a movie, novel, memoir, or even a short story lacks a character triangle, the plot feels thin, the pacing slow, or the characters underdeveloped. Either the conflict between the characters is not complex enough to truly complicate the plot and move it forward or the characterization is too thin.
Each "source of heat" is typically a character, however only two of the sources of heat must be characters (as Anton Chekhov argued, every story must be centered around two characters). In “Hills Like White Elephants” the third source of heat is the woman’s unborn fetus. The fetus is a character, of course, but an absent, almost invisible one. Nevertheless, like Tracy's function on 30 Rock, the unborn fetus draws the man and woman together into conflict. Therefore, the third source of heat must be something that complicates the relationship and/or produces tension between the two characters — as the fetus does in "Hills."
To produce compelling conflict, it is wise to have characters with different value systems, but abstract concepts or intellectual premises alone rarely work as a third source of heat. It's best to create a third character who embodies that concept or premise.
The “three sources of heat” rule also means that in a short story, the optimum number of primary characters is three. Three characters produce just three relationships that you as the writer must negotiate. Their relationships can be represented by a triangle, where each point of the triangle represents a character. However, the addition of a fourth character produces six relationships you the writer must understand, make distinct, and make play a role in the plot. The number of relationships increases exponentially with each additional character, so a fifth character produces ten relationships, and so on.
If we scale this premise up to the level of a novel with many characters, the rule still applies. Consider Harry Potter, and the many triangles that drive its many conflicts. Harry forms
a triangle with Ron and Hermione. He is also in a triangle with Dumbledore and Voldemort, and in a triangle with Snape and his parents. In the past Snape was in a
triangle with Harry's mother and father.
When Harry and another character are not in a triangle with a third character, there is no conflict. Harry is not in a triangle with Malfoy, and so Malfoy isn't really Harry's antagonist. They may clash occasionally, but it doesn't drive the plot forward. Malfoy is simply Harry's foil, their clashes illustrating what Harry could become if he made different choices.