The aircraft departed Kununurra for Perth using rated take off power and 30 flap. Shortly after reducing power via the Thrust Management System to 800 degrees and raising the flap to 18 degrees, a fire warning for No 3 engine was indicated in the cockpit. As the captain commenced to move the power lever towards Flight Idle, the fire warning stopped. The captain analysed the indication and assessed the warning as false. As the aircraft was too heavy to immediately land at Kununurra, he elected to continue the flight towards Perth, after having ensured that he had suitable landing points available enroute if required. Engineers discovered that a fire detector on the recently fitted engine had come into contact with the engine, and the prolonged, higher power setting on take off had tripped the detector and triggered the warning.