What was found
AFTER CLIMBING TO THEIR ASSIGNED ALTITUDE AT FL400 AND INCREASING SPEED TO MAX CRUISE, THE CREW HEARD 2 LOUD NOISES. AT THE SAME TIME THEY SAW THAT ENGINE 2 PARAMETERS WERE FLUCTUATING INCLUDING DECREASING ROTOR SPEED AND RAPID TEMPERATURE INCREASE. A TEMP EXCEEDENCE MESSAGE OCCURRED AT THIS POINT. THE CREW ACCOMPLISHED SHUT ENGINE DOWN, DECLARED AN EMERGENCY AND RETURNED TO DEPARTURE AIRPORT WHERE AN UNEVENTFUL SINGLE ENGINE LANDING WAS ACCOMPLISHED. TROUBLESHOOTING IS ON-GOING.