John Thornton did not have a permanent home in this book. He moved around doing various things to make money.
When we first meet Thornton in Chapter V, he is living in a camp at the mouth of the White River. We are told at the start of the next chapter that Thornton stayed there because he had frozen his feet. He and some partners had been going to get a raft of logs to bring back to Dawson, but he froze his feet and had to make a camp where he could recover.
But even after he heals, Thornton does not go back and live in Dawson. We are told that he used money from the raft of logs to finance an expedition to the headwaters of the Tanana. We also know that Thornton later goes out with a group of men to look for the lost mine (where they are later killed).
So Thornton doesn't live in any one place, but when we first meet him he is in that camp at the mouth of the White River.