What was found
AIRCRAFT WAS GROUNDED: AT APPROXIMATELY 2300Z, DURING CRUISE AT FL 350 RECEIVED ELECTRONIC CENTRALIZED AIRCRAFT MONITOR "HYD G RSVR OVHT" MESSAGE. WE DID THE ECAM ACTIONS, TURNING OFF PTU AND THE ENGINE 1 HYDRAULIC PUMP. AFTER APPROXIMATELY 25 MINUTES, WE RECEIVED ANOTHER ELECTRONIC CENTRALIZED AIRCRAFT MONITOR FOR "G RSVR OVHT" WHEN THE PUMP AND PTU WERE ALREADY OFF. REMOVED AND REPLACED GREEN HYDRAULIC SYSTEM TEMPERATURE SWITCH PER AMM 29-33-11.