"It did not lead him to meditate upon his frailty as a creature of temperature, and upon man's frailty in general, able only to live within certain narrow limits of heat and cold; and from there on it did not lead him to the conjectural field of immortality and man's place in the universe."
This quote really seems to sum up the theme of this story. The man is too arrogant to realize that he is subject to elements beyond his control. In this way I can definitely relate this to Everyman. Everyman too did not consider the consequences of his actions, and Death comes upon him when he leasts expects it, just like the man in the story. In fact, maybe one of the reasons the protagonist in this story is never named is to give him sort of an everyman quality, like it could happen to any of us. In "The River" Bevel doesn't consider the damage that jumping into the river could possibly due to him and therefore trusts too much that elements beyond his control will work in his favor as well. In "The Machine Stops," humankind puts too much trust in its own ability to survive through something it created, like the man in "To Build a Fire," and is destroyed by forces outside of their control. All of these stories seem to deal with humankind's relationship with nature and how they cannot be arrogant and believe that they are the only one in control of their fate.