In London's story, as in his fiction in general, man is shown in a relentless struggle against nature. The principal question at the heart of "To Build a Fire" is: what abilities do men (and animals) require in order to survive, and what is the source of these abilities?
Determinism is a philosophy that attributes results to things outside human will. Obviously, in London's story, will alone is insufficient to save the man. From the way the man acts, a present-day analysis might judge him to have a learning disability. He is familiar with the mechanics of surviving in the Yukon, but seemingly does not recognize the danger he's in:
He was quick and alert in the things of life, but only in the things, and not in the significance.
The extreme cold--50 below zero Fahrenheit--"impressed him as being cold and uncomfortable," but did not lead him to "meditate upon man's frailty in general, able to live only within certain narrow limits of heat and cold." It is as if the man doesn't think himself capable of dying, or doesn't care.
A deterministic view of human nature would judge the man's mindset as an uncontrollable factor that leads to his death. It is unwise to travel alone in such circumstances in the Yukon, but he doesn't know this or doesn't care. The dog, with its instinctive knowledge, understands the reality of the situation far better than the man does. This brings us to the Darwinist element in the story: the issue of survival of the fittest. Ironically the dog, lower on the evolutionary scale than man, is in this case the fittest to survive. The man knows all about the details of building a fire--of slowly adding larger and larger twigs, and so on--but his mental process is incomplete, and the danger of building the fire under a tree that can collapse upon the fire is unknown to him. He similarly has no awareness of the dog's survival instinct and the fact that the dog, while fearful and obedient in ordinary circumstances, won't allow the man to kill him. Altogether the message of "To Build a Fire" is that all creatures have a drive to continue in this life, but that forces of inherent ability over which we have no control (and which are evidence of determinism and the fact that the fittest survive) decide whether or not a given man, or animal, will live.
If one assumes that the fate of the man trying to light the fire was totally determined by previous actions or his previous life, the connection to social darwinism, or the idea of survival to the fittest is relatively straight forward.
The man ignores all kinds of advice suggesting that he ought not to attempt his journey that day and even more importantly not alone. He even receives warnings of a kind from the dog, but all of them come from people or things that are wiser than he is.
His pride is what leads to his eventual death as he ignores all of the wisdom sent his way and even forgets simple things about how to survive in the wild.