What was found
BHM - FLT 1985 - EN ROUTE FROM DFW-CLT, AT FL370, THE NR 2 ENGINE EGT INDICATED OVER 1,000 DEGREES AND THE RED OVERTEMP LIGHT ILLUMINATED. CAPTAIN BACKED OFF THE POWER TO IDLE AND THE EGT DROPPED TO WITHING NORMAL LIMITS. WHEN THROTTLE WAS ADVANCED, EGT WOULD AGAIN CLIMB TO EXCEED LIMITS AND LIGHT WOULD AGAIN ILLUMINATE. ALL OTHER ENGINE PARAMETERS STAYED WITHIN LIMITS DURING EPISODE INCLUDING VIBRATION. FLIGHT DIVERTED TO THE BMH WITH THE NR 2 ENGINE AT IDLE. FLIGHT LANDED WITHOUT FURTHER INCIDENT. NO EMERGENCY WAS DECLARED AND NO ENGINE SHUTDOWN OCCURRED. MAINTENANCE REMOVED, CLEANED AND REINSTALLED INTERFACE CONNECTIONS ON THE NR 2 ENGINE.