I feel that a theme (main idea) of London's "To Build a Fire" is a theme that he frequently uses in his writings. That theme is the theme of nature's indifference to humans. Granted, the man ignored advice to not go out, because he figured he was good enough, strong enough, and smart enough to conquer nature. That wasn't the case, and the man paid the ultimate price. I would be tempted to believe that the main idea being stressed to readers is "be prepared," but the dog ruins that for me.
Then it turned and ran along the trail toward the camp it knew, where there were the other food providers and fire providers.
For me, the dog represents nature. The dog is not human; therefore, he is nature to me. The dog sticks around for a bit after the man dies, then the dog simply moves on in search of other providers. I feel that this shows a cold indifference on the dog's part. He liked the man, as long as the man could provide something for him. The storm is a lot like the dog. It exhibits a sense of cold indifference to the man's efforts. It doesn't matter how hard the man tries to warm himself and curse at the storm. The storm simply carries on without a care in the world. The story has always reminded me of Crane's poem "A Man Said to the Universe."
A man said to the universe:
“Sir, I exist!”
“However,” replied the universe,
“The fact has not created in me
A sense of obligation.”
In the poem, like in London's story, nature flat out doesn't care about man and his efforts.