Take a story's temperature by studying its tone. Is it hopeful? Cynical? Snarky? Playful?
Ironic, Confessional, Gossipy, Angry, Hopeful
We can think of a bunch more adjectives to describe the tone of the story, these seems to be the dominant emotional tones the narrator is expressing as Miss Emily's story is told. (Keep in mind that it's also the town's story.)
The irony of the story is closely tied to the rose in the title, and to Williams Faulkner's explanation of it:
[The title] was an allegorical title; the meaning was, here was a woman who had had a tragedy, an irrevocable tragedy and nothing could be done about it, and I pitied her and this was a salute…to a woman you would hand a rose. (source)
It's ironic because in the story Miss Emily is continually handed thorns, not roses, and she herself produces many thorns in return. This is where the "confessional" part comes in. Since the narrator is a member of the town, and takes responsibility for all the townspeople's actions, the narrator is confessing the town's crimes against Emily.
Confession can be another word for gossip, especially when you are confessing the crimes of others. (Here one of the big crimes is gossip.) The chilling first line of Section IV is a good representative of the elements of tone we've been discussing so far: "So the next day we all said, 'She will kill herself'; and we said it would be the best thing." This is where the anger comes in. Because this makes us angry, we feel that the narrator too is angry, particularly in this whole section. This leads us back to confession and hopefulness.
The hopefulness of the town is the hardest for us to understand. It comes in part from the title again – if we can put ourselves in the same space as Faulkner and manage to give Emily a rose, to have compassion for her even though she is a murderer, to recognize her tragedy for what it is, this might allow us to build a more compassionate future for ourselves, a future where tragedies like Emily's don't occur. This also entails taking off our "rose-colored glasses" (as we discuss in "What's Up With the Title?") and facing the ugly truths of life, even confessing our shortcomings. Hopefully, we can manage to take those glasses off before death takes them off for us.