On April 4, 2014, about 1014 eastern daylight time, a Piper PA-28-161, N642FT, experienced an engine compartment fire after landing at Melbourne International Airport (MLB), Melbourne, Florida. The certified flight instructor (CFI) and pilot-rate student were not injured. The airplane was substantially damaged. The airplane was registered to and operated by FIT Aviation, LLC, under the provisions of 14 Code of Federal Regulations (CFR) Part 91 as an instructional flight. Visual meteorological conditions prevailed at the time and no flight plan was filed for the local flight, which originated about 1 hour 4 minutes earlier. The CFI stated that after landing on runway 27R, while taxiing off the runway onto taxiway "Q" just prior to the hold short lines, the engine quit. He contacted the tower and asked for permission to push the airplane completely off the runway to give himself, "…time to think", but the tower controller declined and instructed them to advise whether they could start the engine. They used the procedures for a hot and cold engine, but was unable to start the engine. They began to notice smoke coming from the engine cowling, and secured the airplane. After evacuating it, they noticed flames from the engine cowling. The CFI attempted to extinguish the fire using the on-board hand held fire extinguisher, but was unable. Airport fire rescue responded and extinguished the fire. During repairs of the airplane to return it to service, the engine mount was inspected and overhauled; however, the firewall required replacement. The carburetor, a MA4-SPA, part number 10-5217, serial number CK47312 was removed, and taken to a FAA certified repair station for inspection and testing with FAA oversight. According to the report, the examination of the carburetor revealed the unit exhibited charring on the exterior and also inside the carburetor throat or venture. Bench testing revealed no issues related to the float shut off and accelerator pump discharge. The removal torque forces of the throttle body to bowl screws were checked and all were reported to be greater than 10 inch pounds, although the technician recalled the values were between 25 and 35 inch pounds (tightening torque specification is 35 to 45 inch pounds). Personnel of the repair station indicate it is not unusual for units in service returned to them for overhaul to exhibit no loosening torque values of the screws that secure the throttle body to the carburetor bowl. Review of the maintenance records revealed the carburetor was overhauled last on December 13, 2013, and installed on the accident airplane on March 21, 2014, where it remained installed until removed postaccident. The carburetor had accrued approximately 37 hours since overhaul at the time of the engine fire. Review of the Pilot's Operating Handbook and FAA Approved Airplane Flight Manual revealed that it specifies that engine fires during start are usually the result of overpriming.