Throughout his literature, Jack London loves to write about dogs. He particularly loves to talk about dogs that are half-wolf because they symbolize the cross between civilization and wildness that characterizes the white north. Or at least, that's what he thought.
In Call of the Wild, London writes about a dog named Buck (although he isn't technically half-wolf) rediscovering his animal instinct in the Yukon after living a life of luxury on a California plantation. In the novel, Buck also forms a very close bond with a man named John Thornton.
But in "To Build a Fire," there "is no keen intimacy between the dog and the man" (16). The dog is just a "toil slave" that wants to be out of the cold, and it looks upon the man as a provider of food and fire, interchangeable with all the other humans who could provide these things. The man, on the other hand, is perfectly willing to use the dog's guts as a hand-warmer if he needs to. It's hardly the bromance of the century.
All we really know about the dog is that it follows at the man's heels and that it wants him to settle down somewhere and stay with a fire (which is a brilliant idea if you ask Shmoop). The dog obeys the man not only because he provides fire and food, but also because "the only caresses [the dog] had ever received were the caresses of the whiplash and of harsh and menacing throat sounds that threatened the whiplash" (16). In this quote, we are reminded that there is no love at all in the dog's obedience to the man, only violence and self-interest.
The wolf dog also symbolizes a connection to instinct, which lies in a "mysterious prompting that [arises] from the deep crypts of its being" (13). This is a knowledge that lies beyond the realm of human understanding—it's mysterious and primal. London describes as a form of awareness genetically inherited from one's animal ancestors: "But the dog knew [of true cold]; all its ancestry knew, and it had inherited the knowledge" (16). It's sort of like reincarnation, but a little more believable.