One narrative technique employed by the story is the use of a first person objective narrator. This means that the narrator is a participant in the events that take place—he is, in fact, the father of a young boy called Schatz who gets the flu and thinks he's going to die—and that he narrates these events after they have already taken place. He uses the first person pronoun "I" as well as past tense verbs, and these help us to identify the point of view.
Using this narrator allows for the misunderstanding that compels Schatz to believe that he is going to die of his illness. The narrator, his father, can only report what Schatz says or how he looks because the narrator does not know the boy's unspoken thoughts or feelings (as a different perspective narrator might), and so he does not realize that Schatz thinks he's going to die as a result of his fever (the boy is comparing his Fahrenheit thermometer reading to a Celsius thermometer reading).
Another narrative technique employed is the elimination of phrases like "he said" or "I said" in many places where there is dialogue. This means that there are fewer words and there are often no words in between characters' speech to one another. This lack makes the dialogue seem more stilted, more abrupt than it typically would. It leaves us with the sense that there is a lot unsaid which, of course, there is. The reader and narrator both don't find out until the end what Schatz has been thinking, but not verbalizing, throughout the story.