What is a great physical challenge similar to that of the protagonist in "To Build a Fire?"
The protagonist of "To Build a Fire" is performing his physical challenge passively; that is, his survival depends on his ability to keep his body warm, not on his ability to achieve great physicality. He doesn't have to run a great distance in a short period of time, but only to keep moving and prevent his clothing from getting wet. In that sense, although the intense cold of the Yukon is certainly challenging, he is not performing a physical challenge such as climbing a mountain or diving to great depths. The challenge is survival by caution, not distance, time, or repetitions.
In a month no man had come up or down that silent creek. The man held steadily on. He was not much given to thinking, and just then particularly he had nothing to think about save that he would eat lunch at the forks and that at six o'clock he would be in camp...
(London, "To Build a Fire," jacklondons.net)
A comparable journey, no less hazardous, would be to cross a hot desert with little water. Like the story, a person would need to be intelligent and forewarned about the intense heat; without water, a person can dehydrate and die from sunstroke or heat exhaustion in a matter of hours. To cross the desert, the man would need loose-fitting clothing, preferably white or tan, and something to cover his face during dusty winds. He would need to keep his skin covered or screened against the sun, which can cause painful sunburn and even melanomas. He would need to keep his pace slow and steady, not over-exerting, because this causes sweating and loss of water. Most importantly, he would need water on his person and know the locations of water on his path; without water, even if a person only travels in the early morning and late dusk, he would be hard-pressed to survive. While London's protagonist knows the hazards of letting his clothing become wet, this hypothetical desert-walker would know the hazards of exposing his body to the sun, and of excessive sweating.