For most of this poem, Eliot uses fire to describe the hellish experience of having to live in the modern world, a.k.a. the waste land. You can see this in lines 308-311, where the speaker starts screaming about the "Burning burning burning burning" and begs for the Lord to just let him die ("Thou pluckest me out"). Later in the poem, though, there is a slight hint that fire might actually be a redeeming or purifying thing. This hint comes mostly from another reference to Dante in line 428, which is written in Italian and means, "he hid himself in the fire which refines them." The possibility that fire can be "refining" gives us some hope that all of the cultural catastrophes we've suffered might lead to something new and good. But it's a vague hope at best.
Lines 82-84: At this point in the poem, we get our first direct image of fire. But the image hasn't yet taken on the significance that it will have in "The Fire Sermon" and onward. This is because early in the poem, Eliot's images are much grayer, with little life in them. He holds off on making us think of Hellfire. The "flames of the sevenbranched candelabra" (82) in this instance serve to show the glitter of the jewels in a lavish, classically beautiful room, which Eliot explores to show how the beauty of the past has been ruined in the 20th century.
Lines 108-110: The meaning of these lines is really ambiguous, since it is unclear whether the image of the woman spreading her hair out in "fiery points" is a good thing or bad thing. The next line (110) suggests that a certain beauty in this woman's fiery hair "Glowed into words, then would be savagely still," which might mean that the fire of her hair is beautiful, but when we try to put it in words, the meaning leaps up for only a second, before dying like a flickering flame. This could represent Eliot's view of classic beauty in the modern era. In other words, Eliot could be arguing that even if classic beauty were able to exist today, it would only appear for a second before getting snuffed out.
The Fire Sermon: Surprise surprise, the fire imagery takes center stage in "The Fire Sermon." This name is a reference to a sermon that the spiritual leader Buddha used to teach people to resist their worldly appetites for sex, power, and material possessions. In this case, fire represents the hunger in modern people that can't be satisfied. All we do is consume, consume, consume without ever really thinking about any larger issues surrounding all our consumption.
Lines 308-311: Out of nowhere, you suddenly read "Burning burning burning burning / O Lord thou pluckest me out" (308-309). Yowza. In these images, you get a sense that the speaker of the poem wants to be pulled out of the world of filthy desires. He doesn't want to chase after sex and material possessions anymore, but wants to be "plucked out" from the world by a higher power like God. It's a very intense way to end a section of the poem, but then again, Eliot's pretty intense when it comes to living a more peaceful life.
Line 322: The "torchlight red on sweaty faces" is the image Eliot uses to open the final section of the poem. The waste land is clearly hot place with no water, but the mention of torches also has Biblical connections to the period following the crucifixion of Jesus Christ: a terrible death, but also a symbol of rebirth.
Line 428: After using fire as a symbol of lust and spiritual damnation, Eliot actually uses it in a potentially positive way in the final lines of the poem. Quoting from Dante, he writes a line in Italian which translates as "he hid himself in the fire which refines them" (428). This line suggests that fire might have the power to refine or clean something instead of destroying it. Maybe for Eliot, rebirth can happen only after something like—let's just say society—has been completely destroyed or "burned up."