What role does the man play in this short story?

Trying to survive.

The man

The man in "To Build a Fire" is purposely not given a name, as the deterministic environment is more important than his free will and individuality. His goal at the start of the story is to reach the camp to meet "the boys," presumably to prospect for gold. The man's greatest deficiency, leading to his death, is his inability to think about the future consequences of present actions or facts; at the beginning of the story, London describes how the extreme cold does not make the man meditate upon mortality. More pertinently, the man does not realize that building a fire under a spruce tree may be dangerous. In all his actions, the man exercises only intellectuality--he thinks about the temperature in terms of degrees Fahrenheit, for instance, a scientific indicator. He never uses instinct, which would inform him without thinking that certain actions are dangerous. The dog, conversely, instinctively understands the danger of the cold without knowing what a thermometer is. Ultimately, the man's lack of free will exonerates him from any deep responsibility for the accidents he has, which is why London writes that the second accident was his "own fault or, rather, his mistake." A "fault" implies full responsibility, whereas a "mistake" suggests an isolated incident out of one's control.

Well said Aslan!

Nice explanation Aslan!