On October 24, 2015, about 1515 central daylight time, a Piper PA 28-235 airplane, N3979X, emitted smoke from under its cowling during touch down on runway 36 at the Courtney Plummer Airport (9WN1), near Winneconne, Wisconsin. The airplane landed and subsequently sustained substantial damage when it caught on fire. The pilot and passenger were uninjured. The airplane was registered to and operated by the pilot as a 14 Code of Federal Regulations Part 91 personal flight. Day visual meteorological conditions prevailed along the route of flight about the time of the accident and the flight did not operated on a flight plan. The flight originated from the Aurora Municipal Airport, near Aurora, Illinois, about 1330 and was destined for 9WN1.According to pilot's accident report, he reported that he could tell something was wrong as he started the descent. The engine was running "rough." The engine "quit" as he touched down. Black smoke and fire exited out of the cowling. He and his passenger opened the door and exited the airplane. The pilot, age 62, held a Federal Aviation Administration (FAA) private pilot certificate with airplane single-engine land and instrument airplane ratings. He also held a FAA third-class airman medical certificate, with a limitation for corrective lenses. The pilot reported on his accident report that he had accumulated 2,800 hours of total flight time in single engine airplanes, of which 10.3 hours were flown in the last 90 days. According to information he provided to the FAA, the pilot indicated he had accumulated 2,900 hours of total flight time, of which 2,000 hours were flown in the same make and model as the accident airplane. N3979X, was a 1975 model Piper PA 28-235 single-engine, low wing, four-place, fixed tricycle landing gear airplane with serial number 28-7610002. The airplane was powered by a 235-horsepower Lycoming O-540, six-cylinder, normally aspirated, reciprocating engine. According to the airplane's type certificate data sheet, the airplane had a fuel capacity 84 gallons, of which 50 gallons were contained within 2 wing tanks and 34 gallons were contained within 2 tip tanks. The airplane's last annual inspection was completed on January 7, 2015. According to copies of airplane airworthiness records and logbook endorsements supplied by a repair station, on April 1, 2015, the airplane had some of its airframe skin repaired, the airplane was repainted, and its tip tanks were leak checked and reinstalled. FAA inspectors examined the wreckage and documented the damage. According to the inspectors and review of images of the wreckage, the airplane sustained discoloration, deformation, and thermal damage that consumed a section of the right side of the fuselage forward of the empennage, the cockpit, and the engine cowling. There was an observed separation in the fuel line going to the carburetor. The fuel line and its fittings were sent to the National Transportation Safety Board (NTSB) Material Laboratory for examination. An NTSB chemist conducted a detailed examination of the fuel line. The examination revealed the separation of the fuel line was consistent with bending overstress with evidence of exposure to high temperature. The chemist's examination did not identify a source of ignition in reference to the fuel line and the investigation did not identify a source of ignition in the remaining wreckage.