As reported to the FAA. Reports are unverified, and codes are left as the FAA publishes them.
What was found
AFTER DEPARTURE FROM HNL, PILOT SHUT DOWN RT ENGINE BECAUSE THE TGT WAS CLIMBING. THE ENGINE WAS SHUTDOWN AT 540TGT. THE PILOT DECLARED AN EMERGANCY AND RETURN TO HNL. AFTER MAINTENANCE LOOKED AT THE A/C, THE PROBLEM WAS THE TOP TEMP ACTUATOR.