"To Build a Fire" by Jack London is narrated in the third person and follows the story of a newcomer to the Yukon who decides to travel alone with a dog to visit another settlement. Although we do find out that an old-timer who had lived in the area and had more experience of it warned him not to make the journey, there really are no other characters in the story. Therefore there are no central interpersonal conflicts.
In the story, there are three major conflicts as the character struggles, unsuccessfully, to complete his journey. The first conflict is with the external environment, particularly the weather. The major enemy is the cold, which causes frostbite and eventually death.
The second conflict is internal, one of not succumbing to fear or inertia. Finally there is a struggle with the dog, who actually has much better instincts than the man himself.
There is an obvious external conflict in the story, To Build a Fire. which is man vs. nature. The "Newcomer" as he is referred to is battling the harsh temperatures for the entire story and trying to stay alive by building a fire. He struggles with wet feet, matches, snow, even the dog, in his attempts to combat the cold. An internal conflict would be his underestimation of his own ability to stay alive in such extreme weather: he ignored advice of the Old Timer who warned him that the temperature was too cold. Additionally, he had never traveled this route before, so he in essence was in conflict with himself (not recognizing his limitations).