On July 29, 2016, about 1300 Eastern daylight time (EDT), a Piper PA-28-161 airplane, N601FT, experienced a total loss of engine power during the landing roll at Merritt Island airport (COI) in Merritt Island, Florida. During the engine restart a fire ensued, and the firewall sustained substantial damage. The flight instructor and student pilot did not sustain injuries. The airplane was registered to American Air Academy Inc. and was operated by the flight instructor as a visual flight rules (VFR), local, instructional flight under the provisions of 14 Code of Federal Regulations Part 91. Visual meteorological conditions prevailed for the flight, no flight plan was filed. The flight originated from COI, Merritt Island, Florida about 1150 EDT. The flight instructor reported that he and his student were practicing takeoff and landings in preparation for the student pilot's first solo. On their seventh landing the engine experienced a total loss of power during the landing roll. The flight instructor further reported that he attempted to restart the engine, but during that process he smelled and observed smoke coming from the engine cowling. He switched off the electrical equipment, secured the fire extinguisher, and attempted to extinguish the engine fire. According to the operator, the carburetor was overhauled about 400 hours prior to accident. A representative of the company that overhauled the carburetor reported that they did not have any records of the overhauled carburetor. The wreckage was sold by the insurance company to a private buyer, and the insurance company did not provide contact information for the buyer. The carburetor was not examined. In the emergency section of the pilots operating handbook under engine fire during start, the procedure is: 1. Starter…………………..Crank Engine 2. Mixture…………….…..Idle Cut-Off 3. Throttle………………...Open 4. Electric Fuel Pump…….Off 5. Fuel Selector……………Off