A DORNIER 328J IN CRUISE AT FL280 DECLARED AN EMER AND DIVERTED DUE TO R ENG HIGH TEMP AND VIBRATION. ACFT ON MAINT FERRY FOR R ENG TEMP EXCEEDANCE.

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THIS ASRS RPT COVERS 2 EVENTS THAT HAPPENED DURING THE ATTEMPT TO FERRY AN AIRPLANE FROM ZZZ-ZZZ1 AN ABORTED TKOF AND A SUBSEQUENT EMER AFTER A SECOND ATTEMPT TO DEPART LATER IN THE DAY. THIS WAS A MAINT FERRY FLT FROM ZZZ TO ZZZ1 CONDUCTED UNDER PART 91 AND THE ONLY OCCUPANTS OF THE ACFT WERE THE FO AND MYSELF. THE R ENG HAD BEEN WRITTEN UP FOR AN ITT ZONE C TEMP EXCEEDANCE; WHICH WAS THE PURPOSE OF THE FERRY FLT. WE ATTEMPTED A TKOF BUT ABORTED BECAUSE THE ITT TEMP HAD AGAIN EXCEEDED A LIMITATION BY REACHING 950 DEGS. WE RECEIVED A CAS MESSAGE CONFIRMING THAT THE LIMITATION HAD BEEN EXCEEDED. WE NOTIFIED TWR AND CLRED THE RWY AND WERE THEN HANDED OFF TO GND CTL. WE REQUESTED TO HOLD OUR POS WHILE WE CONTACTED MAINT CTL AND INFORMED THEM OF THE ABORT AND THE EXCEEDANCE MESSAGE. WE RETURNED TO THE GATE AND I MADE A NOTATION IN THE LOGBOOK CONCERNING THE EXCEEDANCE AND LEFT THE AIRPLANE WITH MAINT. WE THEN WAITED FOR MAINT TO CONDUCT SOME ENG RUN-UPS. WHEN I WAS INFORMED THAT THE AIRPLANE WAS READY TO DEPART AGAIN FOR COLUMBIA; I WAS TOLD BY MAINT THAT THE LOGBOOK NEEDED TO BE CORRECTED AND THAT I HAD WRITTEN UP THE EXCEEDANCE IN ERROR AND THAT THE MAINT FERRY FLT PERMIT AND PREVIOUS WRITE-UP COVERED THE EXCEEDANCE. I WAS GIVEN THE LOGBOOK AND I MADE THE CORRECTION. I CROSSED OUT MY WRITE-UP AND WROTE THAT IT WAS WRITTEN IN ERROR AND THEN SIGNED MY NAME TO IT. I WAS UNDER THE DIRECTION OF MAINT AND DID NOT REALIZE THAT I HAD DONE ANYTHING WRONG AT THE TIME. I WAS CONTACTED BY OUR SAFETY DEPT WHO REQUESTED MORE INFO. THROUGH OUR CONVERSATION; I REALIZED THAT MY ACTION WAS NOT CORRECT AND I SHOULD HAVE LEFT THE NOTATION IN THE LOGBOOK. AFTER RECEIVING THE LOGBOOK AND MAKING THE CORRECTION TO MY PREVIOUS ENTRY; WE ATTEMPTED TO DEPART FOR ZZZ1 ONCE AGAIN. ON THE TKOF ROLL DURING THE SECOND ATTEMPT WE NOTICED THE ITT RISING ON THE R ENG BUT WERE ABLE TO SMOOTHLY ADVANCE PWR AND THE TEMP REMAINED WITHIN LIMITS. WE CONTINUED TO CLB AND PROCEEDED ON COURSE AND NOTICED THAT THE R ENG FUEL FLOW WAS ABOUT 100-200 LBS PER HR GREATER THAN ON THE L ENG AND OPERATED WITHIN 50-35 DEGS BELOW RED LINE AT THE NORMAL CRUISE SETTING. WE WERE ABLE TO REACH OUR CRUISE ALT OF FL280. I CONTACTED OUR MAINT CTL ENRTE TO INFORM THEM OF OUR OBSERVATIONS AND WE WERE TOLD THAT THOSE INDICATIONS WERE AS EXPECTED DUE TO THE NATURE OF THE R ENG EXCEEDANCE. WE NOTICED A FUEL IMBAL SHORTLY AFTER DEP THAT CONTINUED TO INCREASE ENRTE. WHEN IT REACHED 200 LBS; WE DECIDED TO XFEED FROM THE L ENG TO THE R AND AS SOON AS WE TURNED THE XFEED VALVE TO THE OPEN POS; THE R ENG BEGAN TO VIBRATE AND THE ITT ROSE TO 920-950 DEGS. WE STOPPED XFEEDING IMMEDIATELY AND THE VIBRATION STOPPED. WE CONTACTED MAINT CTL AGAIN TO DISCUSS THE PROB; THEN THE VIBRATION OCCURRED AGAIN -- ABOUT 5 MINS LATER AND IT OCCURRED THIS TIME WITHOUT ANY ATTEMPT TO XFEED OR MAKE ANY THRUST LEVER MOVEMENTS. AT THAT POINT; WE DECLARED AN EMER AND REQUESTED TO DIVERT TO ZZZ2. AS WE DSNDED AND THRUST WAS REDUCED; THE VIBRATION STOPPED. THERE WERE NO EXCEEDANCE MESSAGES OR VIBRATION MESSAGES; SO I ELECTED TO KEEP THE ENG RUNNING. WE WEREN'T SURE HOW SERIOUS THE ENG PROB WAS OR HOW LONG IT WOULD LAST AND BECAUSE WE COULDN'T DO ANYTHING ABOUT THE FUEL IMBAL; WE THOUGHT THE BEST COURSE OF ACTION WAS TO DECLARE AN EMER AND DIVERT TO ZZZ2. ATC CLRED US DIRECT TO ZZZ2 AND WE BEGAN ACCEPTING VECTORS TO ALLOW US TO DSND. WE CONTINUED AND LANDED AT ZZZ2 WITHOUT ANY FURTHER PROBS. I KNEW ON THE TKOF ROLL THAT THE ENG HAD THE POTENTIAL TO OVERTEMP AS IT HAD DONE PREVIOUSLY BUT APPLIED THRUST AT A SLOWER RATE AND WE TOOK OFF WITH THE ENG BLEEDS OFF WITH THE APU RUNNING THE PACKS IN THE HOPE THAT THIS WOULD HELP KEEP THE ITT WITHIN LIMITS. AFTER DEP; WE BROUGHT BOTH ENG BLEEDS ON AND SHUT DOWN THE APU AND WERE STILL ABLE TO KEEP THE ITT WITHIN LIMITS. IT MAY HAVE BEEN BETTER TO RETURN TO ZZZ WHEN WE NOTICED THE SIGNIFICANT INCREASE IN FUEL FLOW AS COMPARED TO THE L ENG. THIS INCREASE IN FUEL FLOW LED TO THE IMPENDING FUEL IMBAL THAT CAUSED US TO XFEED AND CREATE THE ENG VIBRATION THAT LED TO US DECLARING AN EMER LATER ON. BECAUSE THIS WAS A MAINT FERRY FLT; I EXPECTED TO SEE ABNORMAL ENG PERFORMANCE AND MAY HAVE ACCEPTED IT FOR A LONGER PERIOD OF TIME THAN I SHOULD HAVE.