The title "To Build a Fire" foreshadows the main obstacle that the man must overcome to survive. Despite the extreme cold, the man is unprepared, and so only brings one source of fire: matches. When he experiences frostbite on his fingers and is unable to handle the matches properly, he finds that he cannot build a fire to thaw out; he must thaw his fingers to build the fire to thaw his fingers. This end is foreshadowed earlier, when he stops for lunch:
He tried to take a mouthful, but the ice-muzzle prevented. He had forgotten to build a fire and thaw out.
(London, "To Build a Fire," eNotes eText)
This directly anticipates his later inability, quoting the title and showing how important fire is in the Yukon. The first mistake only causes him to lose a few minutes at lunch; the second, compounded by an unforeseeable accident, costs him his life.