The central conflict is that between man and nature. In this case the idea that man has invented incredible machinery that can govern almost every facet of life but still cannot control the forces of nature. Though it is not explicit, it appears that mankind has been completely wiped out through some kind of nuclear holocaust and the house has continued to function as a servant to mankind.
But it too cannot escape the forces of nature, in this case the fire that destroys it. So the power of man, manifest through these automated machines, is eventually completely wiped out by the inevitable forces of nature.