ACR MDT INFLT ENGINE SHUTDOWN DUE HIGH ACCESSORY GEAR BOX TEMPERATURE. SUBSEQUENT DEP AFTER ADDING OIL TO GEAR BOX; BUT WITHOUT MAINTENANCE SIGN OFF.

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DURING CRUISE; I GOT AN ACCESSORY GEARBOX LIGHT (RED). PROC CALLS FOR ENG SHUT DOWN. WE SECURED THE ENG AND NOTIFIED ATC. THEN PROCEEDED TO OUR DEST (LCK) WHICH WAS 100 NM AWAY. WE MADE AN UNEVENTFUL LNDG. I SECURED THE PLANE AND CALLED MY FLT FOLLOWING DEPT AT DFW WHO THEN HAD MAINT CALL ME. MAINT SUGGESTED I CHK THE GEARBOX OIL; ADD IF NEEDED THEN RUN UP THE ENG. I ADDED 1 QT OF OIL AND RAN UP THE ENG. THE LIGHT DIDN'T COME BACK ON; THE PROB APPEARED TO BE SOLVED. WE HAVE NO LCL MAINT IN LCK SO UPON DFW MAINT TELLING ME THE PROB WAS NOW SOLVED; WE SUBSEQUENTLY DEPARTED AND RETURNED TO RICHMOND; OUR BASE. UPON ARR I ENTERED THE SHUTDOWN IN THE ACR BOOK AND ADVISED OUR LCL MAINT AT RIC AND DFW. THE PROB WAS CORRECTED AND SIGNED OFF. MY PROB: I SHOULD HAVE STAYED ON THE GND IN LCK AFTER THE SHUTDOWN AND FORCED OUR DFW MAINT TO ARRANGE FOR AN INSPECTION AND SIGN OFF PRIOR TO DEP. I HAVE SINCE MET WITH OUR DIRECTOR OF OPS; CHIEF PLT AND MAINT TO COMPLAIN ABOUT THIS AND TOLD THEM THAT I WILL STAY ON THE GND NEXT TIME.