Compare and contrast Mildred and Montag in Fahrenheit 451.

While Mildred and Guy Montag are alike in that they are both conditioned products of their society, there are still remnants of genuine feeling, desire, and intellectual curiosity in Montag, whereas Mildred has become a virtual automaton, unable to respond to poetry or anything that Montag reads to her.

The fact that Montag has been stealing books for years and hiding them in his house suggests that there are still embers of human sensitivity and spiritual hunger that burn in his soul. Even his enjoyment of the destructive fire demonstrates creative feeling as he imagines the burning books as "flapping pigeon-winged books" that go up "in sparkling whirls"(Part 1). Furthermore, when he meets Clarisse McClellan, Montag demonstrates his perceptive powers and sensitivity as he notices in the girl's face "a kind of gentle hunger that touched over everything with tireless curiosity."

On the other hand, Mildred relies on the parlor walls for thought. Along with her inane friends, Mildred reads scripts for the shows they watch. Despite her devotion to activities like watching the parlor viewing screens, driving fast, and killing animals, Mildred, like Montag, is not happy. However, she has lost too much of her humanity to reclaim it through books (as Montag does). When Mildred's husband reveals to her that he has been hoarding books,

Mildred backed away as if she were suddenly confronted by a pack of mice that had come up out of the floor. He could hear her breathing rapidly and her face was paled out and her eyes were fastened wide. . . . He caught her, shrieking. He held her and she tried to fight away from him, scratching (Part I).

Unfortunately, Mildred has become so conditioned by her society that she betrays Montag, who now pleads with her to help him "figure out why we're in such a mess." Mildred offers no response; she gives Montag no indication of how she feels. Not long after this incident, Mildred commits the ultimate betrayal by reporting her husband for harboring forbidden books.    

What is the difference between Mildred's and Montag's thoughts in Fahrenheit 451?

The point-of-view of the novel is 3rd person limited.  Everything is seen through the perspective of the protagonist, Montag.  Therefore, neither Mildred's thoughts nor the thoughts of any other characters are revealed.  This was done in order to show how Montag alone perceives his surroundings.  Most of his discontent throughout the novel comes as a result of the thoughts he has and his desire to know what others are thinking.  He wants to know he is not alone.  Instead of a "coming-of-age" novel, Fahrrenheit 451 could be classified as a "coming-of-knowledge" novel.

That said, consider this:  Mildred is a shallow character.  Purposefully so.  When she is not sitting in front of her "family" (the soon to be 4-walled television programs) she is plugged in to her "mosquito" ear buds.  It is likely that Mildred does not have any original thoughts, as she fills her ears and head with senseless noise all day (and all night) long.  It is also no wonder when Montag tries to engage her in conversation that has an ounce of depth to it, she cannot respond.  Consider when Montag asks her, "When did we meet, and where," she cannot even remember.

Montag's thoughts, on the other hand, progress throughout the book.  The opening line, "It was a pleasure to burn," is then paralleled by his initial nervousness around Clarisse.  He seems to take his job seriously and Clarrise presents a threat.

His initial sense of threat however progresses to his replaying conversations with her in quiet moments and eventually missing her.  His thoughts then turn to the books he is hiding and the slight sense of fear, but the greater sense of purpose and power that comes with this secret.  Once he begins meeting regularly with Faber we see Montag's thoughts take on a more philosophical air as begins to see himself partly as Faber.

By the end of the novel, Montag's thoughts have lost the fear and confusion they had at the beginning of the story.  He makes decisions with confidence because he has gained a sense of knowledge throughout the book that affords him power, and his thoughts reflect this.