Beatty gives Montag a few hints that he (Beatty) is suspicious that Montag is becoming curious about books and literature. Beatty gives these hints in the hopes that Montag will feel like this curiosity is a common, but temporary phase. Beatty then hopes his hints will imply that Montag has a limited amount of time to reform his behavior.
One of the most significant hints is near the end of "The Hearth and the Salamander." Beatty tries to minimize Montag's possible curiosity by saying that all firemen go through a phase when they wonder:
"One last thing," said Beatty. "At least once in his career, every fireman gets an itch. What do the books say, he wonders. Oh, to scratch that itch, eh? Well, Montag, take my word for it, I've had to read a few in my time, to know what I was about, and the books say nothing! Nothing you can teach or believe!
Montag then asks what if a fireman mistakenly takes a book home. Beatty minimizes the act, saying that it is a natural error and that the fireman has 24 hours before the other firemen will come and burn the book for him. Beatty is suspicious of Montag. Beatty wants to sanitize Montag's curiosity. In other words, Beatty wants to make the allure of books less enticing, less daring, just a phase each fireman goes through. In the end, the hint is also a warning.
Near the end of "The Sieve and the Sand," after Montag returns the book and Beatty burns it, Beatty confirms how useless and misguided books can be:
"Oh, you were scared silly," said Beatty, "for I was doing a terrible thing in using the very books you clung to, to rebut you on every hand, on every point! What traitors books can be! You think they're backing you up, and they turn on you.
At this point, Beatty knows that Montag has other books at home. Here, Beatty is not so much hinting that he still suspects Montag as much as Beatty is trying to convince Montag that he still has the upper hand.