Take a story's temperature by studying its tone. Is it hopeful? Cynical? Snarky? Playful?
In keeping with its focus on matters of life, death, fate, and the relationship between mortals and gods, the Iliad maintains an elevated or lofty tone. This is not to say that it is entirely without humor. The chattering and petty rivalries of the gods are clearly played for comic effect, as are some of the speeches and actions of the mortal characters. All the same, a serious tone is definitely the baseline, and lighter moments play off that.