What was found
AIR TURN BACK DUE TO AFT EQUIPMENT HOT WARNING SHORTLY AFTER TAKE-OFF ON INITIAL CLIMB OUT. NO ABNORMAL INDICATIONS ON ECS SYNOPTIC OR WITH ENGINES. CREW DECLARED EMERGENCY, AND AFTER LEVELING OFF ON INITIAL TURN TO LAND, THE LEFT FIRE BOTTLE DISCHARGED DUE TO EXCESSIVE TEMPERATURES. AIRCRAFT LANDED AT TPA WITHOUT FURTHER INCIDENT. FOUND DUCT SEPARATED FROM LEFT PACK INLET VALVE. INSTALLED 2 NEW COUPLING NUTS ON PACK INLET VALVE AND PROPERLY ATTACHED AND SECURED DUCT. WORK COMPLETED IAW G450 AMM 21-21-00. OPS AND LEAK CHECKS GOOD, NO FURTHER DEFECTS NOTED.