The speaker mentions the "autumn heat" in line 27 in "Burnt Norton," and goes on to make several more references to the four seasons in the poem. The four seasons, of course, are traditionally symbolic of the different parts of a human's life: spring being youth, summer being one's prime, autumn being middle-to-old age, and winter being the final years before death. That said, the fact that there are four seasons also helps provide the speaker with a structuring principle for this poem through the number four.
The most significant use of the seasons in this poem appears in "Little Gidding," which the speaker begins with a meditation on a season he calls "Midwinter spring" (640). Midwinter spring seems to symbolize the little flicker of hope you get even when things are at their darkest (in the middle of winter). You get a little taste of spring, though, which represents the speaker's budding sense of hope, which never makes it past a bud in this poem. Still, for Eliot, that's still a huge thing.
224-225: "What is the late November doing / With the disturbance of the spring"
400: Keeping his seasons and rages, destroyer, reminder"