AN ACR B727-200 FLC HAS BOTH AIR-CONDITIONING PACKS OVERHEAT AFTER TKOF FROM AN ARPT IN MODERATE SNOW CONDITIONS.

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CONDITIONS AT OUR TIME OF DEP WERE CONTINUOUS MODERATE SNOW. EXTERIOR AND COCKPIT PREFLT PREPARATIONS WERE NORMAL AS WE WAITED FOR FUELING AND DEICING OPS TO FINISH. WE RECEIVED OUR DEICING BRIEFING AND HAD A NORMAL PUSHBACK. ALL 3 ENG STARTS WERE NORMAL AND WE COMPLETED OUR 'BEFORE TAXI' CHKLIST. ON TAXI; THE AIR-CONDITIONING COOLING DOORS WERE CLOSED IN ACCORDANCE WITH TAXI OPS IN SNOW AND SLUSH. ALL TAXI AND TKOF CHKLIST ITEMS WERE COMPLETED. I PERFORMED A VISUAL INSPECTION OF THE WINGS AND THEY PROVED TO BE FREE OF SNOW AND ICE. RETURNING TO MY SEAT; THE CAPT GAVE US A FULL TKOF BRIEFING FOR HIS LEG. WE RECEIVED OUR TKOF CLRNC AND 'TKOF FINAL ITEMS' CHKLIST WAS COMPLETED. ACCELERATION AND TKOF WERE NORMAL. ON INITIAL CLBOUT I NOTICED A RAPID INCREASE IN THE ENVIRONMENTAL DUCT TEMP ALONG WITH AN INCREASING TEMP IN THE #2 PACK. I ATTEMPTED TO ADJUST THE TEMP CTLS BUT IT HAD NO EFFECT. I INFORMED THE CAPT AND HE RECOMMENDED TO TURN OFF PACK #2 AND I AGREED. I REFERRED TO THE COM TO WORK THE PROB WITH THE FO. QUICKLY FOLLOWING; THE #1 PACK TEMP BEGAN TO SHOW AN OVERHEAT WHICH COULD NOT BE CTLED. I INFORMED THE CAPT AND HE STATED THAT IT NEEDED TO BE TURNED OFF. I AGREED. WE INFORMED ATC THAT WE WOULD NOT BE ABLE TO PRESSURIZE AND NEEDED A LEVELOFF. I CONTINUED TO WORK THROUGH THE COM WITH THE FO AND IT WAS DETERMINED THAT WE WOULD NOT BE ABLE TO USE THE PACKS. WE PLACED A PHONE PATCH TO OUR COMPANY DISPATCH AND THEY RECOMMENDED A RETURN TO OUR DEP ARPT. ALL COM PROCS WERE COMPLETED AND WE INFORMED OUR CABIN CREW AND PAX OF OUR RETURN. WE INFORMED ATC WE WOULD BE RETURNING AND THAT WE REQUIRED A SHORT AMOUNT OF TIME TO DUMP FUEL TO HELP US MAKE OUR LNDG WT. THE FUEL DUMPING PROC WAS COMPLETED BY THE CHKLIST AT WHICH TIME WE FLEW AN ILS TO A NORMAL APCH AND LNDG. UPON RETURN TO THE GATE; A MAINT INSPECTION REVEALED THAT THE RAM AIR COOLING INLET HAD INGESTED SNOW AND NO COOLING WAS AVAILABLE.