Central Point, Ore. ? Lost in the snowy wilderness and seeking help for his stranded family, James Kim probably traveled more than 10 miles on foot before he died, believing he could find a nearby town, authorities said Thursday.

An autopsy showed that he died alone of hypothermia. Authorities said when his body was found in a creek’s shallow water on Wednesday, he was about a mile away from a fishing lodge stacked with food.

“James Kim did nothing wrong. He was trying to save his family,” Lt. Gregg Hastings of the Oregon State Police said at a Thursday news conference. “He thought that if he could get to the river, he could make it to the town.”

Kim thought the nearby town of Galice was only four miles away, although it was really 15 miles, Hastings said. Just a mile down the road, however, was a fishing lodge where he could have found shelter, warmth and enough food for months.

“It would have been a beautiful ending to a sad story,” said John James, the owner of the nearby Black Bar Lodge.

After scouring the mountains of southern Oregon for days, a search helicopter hired by Kim’s family spotted the man’s body fully clothed on his back in Big Windy Creek near the Rogue River, authorities said. During the search, authorities found several pieces of clothing they believed Kim left as a trail to find him; medical experts said it could be a sign of hypothermia, which can make victims feel warm and shed clothing.

A deputy state medical examiner was unable to determine the exact time of death, Hastings said.

Kim’s wife, Kati, and two daughters were rescued Monday when they were spotted by a search helicopter as they were leaving the car to find help themselves. She told authorities they had missed a turnoff Nov. 25, and after consulting a map, made another turn.

Hastings said Kati told officers it snowed hard several days while the family was stuck, and they heard helicopters at least twice. When help didn’t arrive, James Kim struck out to look for help.

“Kati and the kids are in good condition as it relates to the ordeal that they’ve been through,” Hastings said.