What was found
(CAN) DURING ENGINE START, AT ABOUT 40 TO 50 PERCENT, N2, ALL LIGHTS ON THE ITT TAPE INSTANTLY LIGHTED UP. WE IMMEDIATELY SHUTDOWN ENGINE. RESIDUAL ITT WAS ONLY 56 AND NR9702, AFTER MOTORING. VISUALLY INSPECTED THE ENGINE FOR SIGNS OF HEAT OR DAMAGE AND FOUND NOTHING. SUSPECTED INDICATION PROBLEM AND DECIDED TO TRY ANOTHER START. START WAS NORMAL. WHILE WE CRUISED AT FL 390, ABOUT 50NM SOUTH, NOTICED A HIGH ITT (ALL LIGHTS ON AGAIN) ON THE SAME LT ENGINE. IMMEDIATELY WE REDUCED THRUST TO REGAIN WITHIN LIMITS. ABOUT 5 MINUTES LATER, ITT STARTED RISING GRADUALLY, AGAIN WE REDUCED THRUST. CREW DISCUSSED ALTERNATE PLAN (DIVERTING), ITT STARTED AGAIN. KEPT REDUCING THRUST UNTIL WE HAD TO SHUTDOWN THE LT ENGINE AND DIVERTED. DURING THE WHOLE EVENT, ALL INDICATIONS WERE NORMAL EXCEPT THE LT ITT. LANDING (FLAPS 20 AND NR9702,) WAS NORMAL. AFTER TROUBLESHOOTING THE SIGNAL DATA CONVERTER WAS FOUND TO BE AT FAULT. CONVERTER REMOVED AND REPLACED AND AC RETURNED TO SERVICE. (TC NR 20080109009)