This is an interesting question because the majority of the conflicts are person vs. person or person vs. technology. One way to think about this is to consider Montag's human nature. He has been taught to suppress any "natural" curiosity about literature or critical thinking. Indeed, he is born with the ability to be curious and with the ability to read and think critically. But Beatty and other people in power have brainwashed him to suppress these abilities. So, in a sense, Montag is fighting against his own nature. Upon talking to Clarisse and Faber, he fights through this brainwashing and eventually gives in to his natural curiosity about literature and human thinking. In this case, thankfully, nature wins.
For a more traditional notion of person vs. nature, consider Montag's race to freedom at the end of the book. He runs through people's yards in order to get to the river. He has to risk swimming through the river in order to escape the Mechanical Hound. He does float peacefully down the river, happy to be away from his old life. But when he reaches land, he is overwhelmed with what he has been through and with the journey that awaits him:
He wanted to plunge in the river again and let it idle him safely on down somewhere. This dark land rising was like that day in his childhood, swimming, when from nowhere the largest wave in the history of remembering slammed him down in salt mud and green darkness, water burning mouth and nose, retching his stomach, screaming! Too much water! Too much land!
After all the running and rushing and sweating it out and half-drowning, to come this far, work this hard, and think yourself safe and sigh with relief and come out on the land at last only to find . . . The Hound!
It turns out to be a deer. But these passages shows how Montag does have to struggle against nature during his mad dash to freedom.