AN AIRBUS 310 WAS DISPATCHED IN NON COMPLIANCE WITH HEAT DAMAGE TO THE R AILERON; FLAP PANELS; FLAP TRACK FAIRING; AND ENG PYLON. CAUSED BY RECURRING #2 ENG TAILPIPE FIRE.

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DURING PUSHBACK; THE TUG OPERATOR (MAINT) ADVISED WE WERE 'CLRED TO START ENG.' CREW ENGAGED STARTER FOR #2 (R) ENG AND SELECTED FUEL LEVER ON AT APPROPRIATE TIME. ADVISED 'TAILPIPE FIRE;' FUEL LEVER SELECTED OFF; ENG WAS MOTORED; THEN STARTER MOTOR WAS DISENGAGED. REFERRED TO OUR QRH AND COMPLIED WITH ALL PERTINENT STEPS ON CHKLIST. CREW DID NOT ACTIVATE FIRE BOTTLES; BECAUSE MAINT ADVISED FIRE WAS OUT MOMENTS AFTER FUEL LEVER WAS SELECTED OFF. OUR QRH CHKLIST ADVISED MAINT WAS REQUIRED. CAPT ASKED MAINT WHAT WAS REQUIRED ON THEIR PART. MAINT ADVISED THEY WOULD INSPECT THE #2 ENG AREA AND GET BACK TO US SHORTLY. WHILE MAINT WAS RUNNING THEIR INSPECTION; THE CAPT COMMENTED TO ME THAT THIS WAS A 'REPEAT;' IE; THIS ENG HAD A TAILPIPE FIRE AT STARTUP ON PREVIOUS TRIP. MAINT THEN CALLED ON INTERPHONE; ADVISED INSPECTION WAS COMPLETE; AND WE WERE CLRED TO RESTART #2 ENG. THE SECOND START WAS NORMAL; AND THE FOLLOWING FLT UNEVENTFUL. HOWEVER; MAINT PERSONNEL AT ARR ARPT; WHILE DOING THEIR DAILY CHKS/INSPECTION; DETERMINED THAT THE R-HAND AILERON AND 2 OF THE TRAILING EDGE FLAP PANELS WERE DAMAGED BEYOND ALLOWABLE LIMITS. DAMAGE WAS ALSO FOUND ON A FLAP TRACK FAIRING (CANOE) AND ON A PORTION OF THE ENG PYLON. CAPT ADVISED THAT HE INTENDED TO DO A WRITTEN ENTRY INTO THE MAINT LOG; BUT SIMPLY FORGOT TO DO SO. (IT WAS MAINT AT THE DEP ARPT THAT ADVISED THE CREW OF THE PROB; THEN INSPECTED THE #2 ENG AREA; AND CLRED US TO START #2 ENG (AGAIN); SO WE MIGHT CONTINUE THE OUTBOUND TRIP.) MAINT RECORD NOW ALSO SHOWS MAINT PERSONNEL AT ARR ARPT HAVE ACCOMPLISHED A BORESCOPE EXAMINATION OF ENG AND CHANGED THE FUEL CTL UNIT; WHICH MIGHT HAVE BEEN THE BASIC CAUSE OF THE 2 TAILPIPE FIRES.