What was found
REPORTED BY PILOT: ON FINAL FOR THE RNAV 23 INTO KRZN, I GOT A NR 2 ENG OIL HOT LIGHT. INITIAL COMPARISON OF THE ACTUAL OIL TEMP SHOWED 123, AND STILL IN THE GREEN. THAT LASTED FOR ABOUT 5 SECONDS WHEN THE TEMP STARTED TO CLIMB RAPIDLY TO 127 BEFORE I COULD PLACE THE NR 2 ENGINE INTO IDLE MODE. THE TEMP DID NOT SUBSIDE AND IT’S HIGHEST NOTED TEMP WAS 137 PRIOR TO SHUTTING THE NR 2 ENGINE DOWN COMPLETELY. I CONTINUED THE 4 MILE FINAL IN OEI AND MADE THE APPROPRIATE RUN ON LANDING. FOLLOW ON MAINTENANCE: FOUND OIL COOLER TEMPERATURE REGULATING VALVE TO BE IN-OP. INSTALLED NEW VALVE P/N 728843, OPS CHECKED GOOD AND RETURNED TO SERVICE.