What was found
LEVELING OFF AT FL 370, NOTICED OIL PRESSURE ON RT ENGINE WAS IN AMBER RANGE INDICATING 23 PSI WITH OIL QTY INDICATING 0. SHORTLY, RT ENG OIL TEMP STARTED INCREASING. FOLLOWED QRH FOR LOW OIL PRESSURE. OIL TEMP CONTINUED INCREASING & RAN ENGINE OIL TEMP QRH. INITIALLY, TEMP STARTED COMING DOWN WITH RT ENGINE AT IDLE AFTER ABOUT A MINUTE AT IDLE, TEMP STARTED CLIMBING AGAIN. TO PRECLUDE ENG DAMAGE, SHUTDOWN RT ENGINE IAW QRH. EMERGENCY WAS DECLARED & LANDING MADE WITHOUT FURTHER INCIDENT. FINISHED INSTALLATION OF #2 ENGINE AS PER WC 7100000-02-03, OPS & LEAK CHECKED GOOD ON ENGINE RUN IAW JRH.