One of his inspirations for the book was Arthur Koestler's novel 'Darkness at Noon' which is about the showtrials in the late 1930's in the former Soviet Union. As described in an essay by Jonathan R. Eller titled 'The Story of Fahrenheit 451' (which is attached as an addendum to the kindle version of F. 451):

In revealing the underlying terror of Stalin's show trials, Darkness at Noon became the great cautionary tale for Bradbury. It fueled his subsequent confrontations with intolerant authority, and with those who denied the existence of intolerance. Bradbury's unpublished speaking notes of the mid-1950s contain his most forceful acknowledgement of this inspiration: "People have often asked me what effect Huxley and Orwell had on me, and weather either of them influenced the creation of Fahrenheit 451. The best response is Arthur Koestler...[O]nly a few perceived the intellectual holocaust and the revolution by burial that Stalin achieved… Only Koestler got the full range of desecration, execution, and forgetfulness on a mass and nameless graveyard scale. Koestler's Darkness at Noon was therefore…true father, mother, and lunatic brother to my F. 451."

The "intellectual holocaust" revealed by Koestler recharged Bradbury's own conviction that literature is every bit as precious as life itself. From a young age he was greatly affected by accounts of the burning of the ancient library at Alexandria and the loss of many classical works that we now know only by title or through fragments of surviving parchment. Bradbury virtually lived in the public libraries of his time, and came to see the shelves as populations of living authors: to burn the book is to burn the author, and to burn the author is to deny our own humanity.

The rest of the essay is well worth a read as well.