What was found
(CAN) SHORTLY AFTER TAKEOFF (5 MIN) CLIMBING THROUGH FL080 AN (AMBER) R HYD TEMP HIGH CAS POSTED. CREW ELECTED HYD SYNOPTIC PAGE AND THE RT HYD TEMP DISPLAYED WAS 115C AND RAPIDLY CLIMBING. CREW BEGAN TO PERFORM QRH PROCEDURES AND WITHIN ONE MINUTE RT HYD TEMP HAD CLIMBED TO 158C. QRH INSTRUCTS TO SHUTDOWN ENGI IF HYD TEMP REACHES OR IS ABOVE 155C. CREW SHUTDOWN RT ENG, IAW THE QRH, AND HYD TEMP STABILIZED. CREW DECLARED AN EMERGENCY AND ASKED TO BE DIVERTED. CREW LANDED ACFT WITHOUT INCIDENT. ON POST FLIGHT CREW COULD SMELL AN ODOR OF OVERHEATED OIL AT THE REAR OF THE ACFT. NO SMOKE OR FIRE WAS DETECTED. FOUND DEBRIS IN LT EDP CASE DRAIN FILTER. REMOVED AND REPLACED LT ENG DRIVEN HYD PUMP. REPLACED PRESSURE RETURN AND CASE DRAIN FILTERS AND FLUSHED HYD SYS. REPLACED HEAT EXCHANGER BYPASS VALVE AS A PRECAUTION DUE TO THE AMOUNT OF MATERIAL FOUND IN THE CASE DRAIN FILTER. OPS CHECK AND LEAK CHECK GOOD. ACFT RTS`D.