What was found
(CAN) AIRCRAFT OPERATING WITH #1 AIR CONDITIONING PACK ON DEVIATION DUE TO OVERHEAT. UNABLE TO CONTROL CABIN PRESSURIZATION, TRIED TO RESTART #1 PACK, NO SUCCESS. INITIATED EMERGENCY DESCENT TO 10,000 FEET. MAINTENANCE TROUBLE SHOOTING REVEALED TRIM AIR PRESSURE REGULATOR FAILED. REGULATOR REPLACED AND SYSTEM CHECKED SERVICEABLE.