What was found
PASSING THRU 10000FT RT PACK LIGHT WITH CAUTION ILLUMINATED. RAN QRH PACK LIGHT REMAINS ON. CREW STATES RT PACK LIGHT CAME ON GOING THROUGH 10,000FT. CABIN WAS REALLY HOT SPECIALLY TOWARDS AFT OF ACFT. COCKPIT TEMP COMFORTABLE, AIR WAS WORKING AS NORMAL. THERE IS HISTORY PRESENT. PERFORMED HEALTH CHECK ON #2 ENGINE PRECOOLER CONTROL VALVE IAW AMM 36-12-00-700-801 PRECOOLER CONTROL VALVE SYS HEALTH CHECK. PRECOOLER CONTROL VALVE FAILING STEP 2.G (6) (C) & NOT WITHIN 30 DEGREES OF FULL OPEN WHEN 3 PSI CONTROL PRESSURE IS SUPPLIED TO VALVE IAW AMM 36-12-00-700-801 PRECOOLER CONTROL VALVE SYS HEALTH CHECK. REMOVED #2 ENGINE PRECOOLER CONTROL VALVE IAW AMM 36-12-02-000-801 PRECOOLER CONTROL VALVE REMOVAL. REPLACED #2 ENGINE PRECOOLER CONTROL VALVE THROUGH STEP 3.G AMM TASK 36-12-02-400-801 PRECOOLER CONTROL VALVE INSTALLATION. LEAK CHECKED SENSORS IAW AMM 36-00-00-860-805, NO LEAK NOTED, BITE TEST PACK/ZONE TEMP CONTROLLER IAW AMM 21-61-00-700-806-002.