The novel originally started out as short story called Bright Phoenix that Bradbury wrote in 1947. He later expanded it to a novella titled The Fireman (published in Galaxy Sci Fi 1951) and finally into the novel Farenheit 451. See article. Interestingly, Bright Phoenix wasn't published until the May 1963 edition of the Magazine of Fantasy and Science Fiction.
The quotation from Farenheit 451 referenced in Mistah Mix's answer is (according to Note 1 in this Wiki article) ambiguous and open to interpretation. That same note however also states that the novella sets the time in October 2052.
The full text of the novella is available here. The formatting is 'unkind' but the beginning of the novella is explicit regarding the date -
Fire, Fire, Burn Books
The four men sat silently playing blackjack under a green drop-light in the dark morning. >Only a voice whispered from the ceiling: "One thirty-five a.m. Thursday morning, October >4th, 2052, A.D. . . . One 'forty a.m. . . . one fifty . . ."
Mr. Montag sat stiffly among the other firemen in the fire house, heard the voice-clock >mourn out the cold hour and the cold year, and shivered.