The aircraft took off and departed Darwin with engine bleed air off, utilizing the auxiliary power unit (APU) for air-conditioning. The APU was not shut down immediately after take-off to allow it a longer cooling period. As the aircraft reached flight level 330, the purser noticed a vibration near the rear entry door and advised the flight crew. The first officer investigated the problem, and as he returned to the cockpit the APU fire warning light illuminated, and the fire bell sounded. Fire procedures were carried out, the extinguisher bottle discharged, and the fire warning ceased. The purser also reported that the vibration then ceased. The flight continued to Alice Springs and landed without further incident. Subsequent investigation of the APU revealed evidence of burning near the thermocouple and the APU was replaced.
