What was found
CREW REPORTED, DURING CLIMB THROUGH ABOUT FL230, LEFT OIL TEMPERATURE GAUGE ROSE TO A READING BEYOND THE RED RADIAL. COM PROCEDURE FOLLOWED AND CALL FOR PRECAUTIONARY ENGINE SHUTDOWN. EMERGENCY DECLARED WITH ATC AND RETURN TO DEPARTURE INITIATED. AS POWER LEVER OF LT ENGINE REDUCED TO COMMENCE SHUTDOWN, OIL TEMP BEGAN TO FLUCTUATE, AND RETURNED TO NORMAL RANGE AFTER A FEW SECONDS. CONTINUED FLIGHT WITH BOTH ENGINES AND LANDED WITHOUT INCIDENT. MAINTENANCE AT MAINTENANCE BASE R & R LT ENGINE OIL TEMPERATURE GAUGE IAW AMM 31.01. R & R LT ENGINE OIL TEMPERATURE SENSOR IAW AMM 79-34-01. OPS CHECKED GOOD IAW AMM 71-08 FOR TEMPERATURE GAUGE AND OIL TEMPERATURE SENSOR LEAK CHECKED GOOD.