What was found
HYD G RSVR OVHTIN CLIMB. FOLLOWED ECAM SLIGHTLY DECREASED AND FAULT LIGHT EXTINGUISHED BUT ECAM MESSAGE ALONG WITH OVERHEAT WARNING ON HYDROLIC PAGE ON LOWER ECAM WITH REMAINED. ABOUT 15 MINUTES BEFORE TOUCHDOWN, THEY TURNED LEFT FAULT INDICATIONS ON ENG 1 PUMP AND PTU PBSW. HYDRAULICS BACK ON FOR NORMAL LANDING GEAR OPERATION AND KEPT IT ON UNTIL RETURNING TO GATE WITH NO RETURN OF THE FAULT LIGHT. LOCKED FOR POSITIVE FIX UNLOCKED FOR TECH. LOCKED . UNLOCKING FOR UPDATE RE-LOCKING CREW REPORTED FAULT LIGHT ON ENG 1 PUSHBUTTON AND "OVERHEAT" PERFORMED GVI OF #1 ENG CASE DRAIN FILTER AND FOUND NO FLAGGING AS SDR REF TSM 29-11-00-810-804-A PERFORMED OPERATIONAL TEST OF GREEN REF TSM 29-11-00-810-802-A DURRING PERFORMANCE OF ENGINE AUTO NEXT STEP IS TO CHECK THE INTERNAL LEAKAGE OF THE GREEN HYDROLIC MESSAGE ON HYDRAULIC ECAM PAGE AT 22,000 FT, ABOUT 15-20 MINUTES DISCREPENCIES. HYDRAULIC SYSTEM. DURRING DRY MOTOR, OPS TEST GOOD, PRESSURES START. OPPERATED FLAPS CONSISTANTLY FOR 5 MIN. AFTER OPPERATED SYSTEM REF AMM 29-00-00-280-001 AND THE PTU REF AMM AFTER TAKE OFF. THEY SHUT OFF LEFT HYDRAULICS AND PTU AND AND QUANITY ON GREEN SYSTEM CHECKED GOOD. NO FAULTS NOTED RUDDER, AILERONS,ELEVATOR, AND SPOILERS OF THE GREEN SYSTEM. AT 29-00-00-280-004). TEMPERATURE ABOUT 6 MIN (11 TOTAL) OVERHEAT MSG DISPLAYED ON UPPER ECAM STATE FINDINGS. CONFIRMATION OF FIM 29-11-00-801-802-A.