The only time weather is even mentioned is during the time Montag and Clarisse walk to the corner. On page 28 --- my edition -- you may need to look in the general area in your edition --- it says that:
"One day it was raining, the next day it was clear, the day after that the wind blew strong, and the following day the wind would be mild and calm, and the day after that calm day was a day like the furnace of summer..."
None of these become an issue in the plot. However, if you need it for the exposition, it seems that all kinds of weather would be appropriate. Weather isn't really a part of the exposition as much as place and time. The place would be a large city serviced by a subway (New York is inferred since it has the largest subway system in the United States ) that travels to the suburbs. The time is sometime in the far future. No definite dates are given. Remember, this book was written in 1953.