Final answer:
The character is externally motivated by the urgent need to dry his feet to prevent frostbite in sub-zero temperatures.
Step-by-step explanation:
The character's motivation in the excerpt from an adaptation of "To Build a Fire" is primarily externally motivated by the need to dry his feet. This is not just a desire but rather an essential survival tactic in the extreme cold, as the text emphasizes the imperative nature of drying his wet foot-gear to avoid frostbite or worse. The urgency is driven by the potentially fatal consequences of not addressing his wet feet in such frigid temperatures.