"To Build a Fire" is ultimately about the struggle for survival in the frigid conditions of the Yukon (in this sense, its primary conflict is one of man versus nature). The dog plays an important role within this thematic context, serving as a foil to the man, even as the two remain in an uneasy partnership that, in both cases, is driven by pragmatism and an interest in survival rather than by any genuine ties of companionship or affection.
For London, the dog, with its animal instincts, remains closely attuned to nature in a way that the man, still ingrained in the experience of civilization, cannot replicate. In this sense, seen within the struggle for survival against nature's overwhelming power, it is the dog that emerges as the man's superior. It is the man who is intent on trekking onwards through dangerously low temperatures (not realizing how severely cold it is), even as the dog's mind turns towards thoughts of warmth.
It is the man who makes the fatal mistakes in his determination to trek onward through these extreme conditions, and, moreover, in his arrogance to disregard all warnings and advice and attempt this journey alone. Meanwhile, it is the dog that retains an awareness of the extreme cold and the danger this represents. Indeed, this thematic contrast London paints between man and dog is perhaps most fully encapsulated in the story's ending, where the man dies and the dog goes on alone.