A B737-300 L PACK CTL FAILED IN FULL COLD CAUSING THE CREW TO BECOME EXTREMELY COLD. DOOR OPENED TO HEAT FLT STATION.

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ENRTE WE HAD A PROB WITH THE L AIR MIX VALVE. EVERY TIME WE TRIED TO COMMAND HEAT FOR THE COCKPIT; THE VALVE WOULD GO 1/2 WAY ON THE INDICATOR AND THEN WE RECEIVED A L DUCT OVERHEAT ANNUNCIATION. THIS OCCURRED IN BOTH 'AUTO' AND 'MANUAL' FUNCTIONS OF THE TEMP CONTROLLER. COCKPIT BECAME VERY COLD. IN FACT; ICE WAS FORMING ON THE INSIDE OF THE MAIN WINDSHIELD AND BOTH THE CAPT AND FO HEATED SIDE WINDOWS. I; IN FACT; WAS EVEN TOWARDS THE SUN AND STILL WE WERE ICING UP. IT GOT TO THE POINT THAT WE WERE BOTH FREEZING AND SHIVERING EVEN THOUGH WE PUT ON OUR JACKETS AND WINTER COATS. THE CAPT DECIDED THAT TO WARM THE COCKPIT; IT WOULD REQUIRE THE OPENING OF THE COCKPIT DOOR. HE INSTRUCTED THE FLT ATTENDANTS TO PUT UP THE CART; AND ONE STAND GUARD AT THE CART AND ONE STAND GUARD AT THE COCKPIT DOOR. WE REMAINED IN THIS CONDITION UNTIL LNDG; EXCEPT THE CART WAS STOWED AND A FLT ATTENDANT WAS PLACED IN THE COCKPIT JUMPSEAT TO ACT AS BARRIER. I CAN SAY THAT I HAVE NEVER BEEN SO COLD BEFORE. IT WAS HARD TO FUNCTION IN THIS CONDITION. OPENING THE DOOR HELPED AND I BELIEVE IT WAS THE RIGHT THING TO DO.