What was found
ACFT DEPARED, AT ABOUT 1300L FOR A 5 MINUTE REPO FLT (NO PAX), WITH APU RUNNING, SHORTLY AFTER LEVEL OFF AT 3000', FIRE WARNING SOUNDED, APU FIRE LIGHT ILLUMINATED, & APU AUTOMATICALLY SHUTDOWN. WARNING LIGHT DID NOT EXTINGUISH & FOLLOWING EMERGENCY PROCEDURES, CREW FIRED APU FIRE BOTTLE. FIRE LIGHT STILL DID NOT EXTINGUISH, REQUESTED PRIORITY & FIRE EQUIPMENT. CREW HAD NO OTHER SYSTEMS AFFECTED & EXPERIENCED NO SMOKE OR FUMES. UPON LANDING & CLEARING RUNWAY THEY SHUT EVERYTHING DOWN. UPON INSP OF AFT COMPARTMENT NO SIGN OF FIRE INDICATED. CREW RE-STARTED 1 ENGINE TO TAXI IN, FIRE LIGHT DID NOT ILLUMINATE. MX PREFORMED A VISUAL INSP OF APU & AFT BAY WITH NO DISCREPANCIES NOTED. DETERMINED ACFT TO BE SAFE FOR CONTINUED OPS & PLACE FOLLOWING ITEMS ON MEL. MEL 26-2 CAT "C" APU FIRE WARNING SYS. MEL 26-3 CAT"C" APU FIRE EXTINGUISHER SYS. PLACARDED INSTRUMENT PANEL & INSTRUCTED THAT "APU MAY NOT BE USED".