ALT OVERSHOT DUE TO DISTR OF UNCOMFORTABLE FLC OF A DC9 THAT HAD PAX HEALTH PROBS DUE TO HIGH CABIN COCKPIT TEMPS OUT OF SAT; TX.

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FO WAS PF AT FL250 TO MCI WITH AUTOPLT ENGAGED. APPROX 160 NM S OF MCI; ATC CLRED FLT FROM FL250 TO FL240 (1000 FT DSCNT). ALT WAS INSERTED INTO ALT ALERTER; COMPANY ALT AWARENESS PROC WAS FOLLOWED; AND FO EXECUTED THE DSCNT VIA THE AUTOPLT PITCH CTL WHEEL. DURING THE DSCNT; #1 FLT ATTENDANT CALLED COCKPIT ON THE INTERPHONE; WHICH WAS ANSWERED BY PNF; CAPT. CAPT'S DISCUSSION WITH FLT ATTENDANT WAS BRIEF (15-20 SECONDS) REGARDING CABIN TEMP CONDITIONS AND THE VISUAL HEALTH OF 1 PAX WHO APPEARED GRAYISH IN COLOR. THIS CONVERSATION WAS FOLLOWED SHORTLY THEREAFTER WITH CODED KNOCK ON COCKPIT DOOR. THE CAPT (PNF) GLANCED AT THE ALTIMETER TO VERIFY PF'S ALT; WHICH WAS WITHIN 300 FT OF THE FL240 LEVELOFF ALT; AND PROCEEDED TO UNBUCKLE; STAND; AND REMOVE THE KATY BAR ON THE COCKPIT DOOR. SIMULTANEOUSLY; AS THE COCKPIT DOOR WAS OPENED; CAPT LOOKED BACK AT THE FO'S ALTIMETER AND STATED; '(NAME) FL240' JUST PRIOR TO THE ALT ALERTER'S 300 FT BELOW SELECTED ALT CHIME SOUNDED. FO IMMEDIATELY DISCONNECTED THE AUTOPLT AND INITIATED A CLB TO CORRECT FOR THE ERROR. IN THE TRANSITION; AN ADDITIONAL 200 FT OF ALT WAS LOST (23500 FT INDICATED) BEFORE A POSITIVE CLB WAS ESTABLISHED AND ACFT WAS LEVELED AT FL240. DURING THE MANEUVER TO RETURN TO FL240; THERE WERE NO TA OR RA TFC DEPICTED; AND NO EVASIVE ACTION CALLED FOR BY THE ONBOARD TCASII. BOTH THE CAPT AND FO WERE DISTRACTED BY A NUMBER OF FACTORS THAT CONTRIBUTED TO THIS INCIDENT. ACFT WAS DISPATCHED WITH 1 AIR-CONDITIONING PACK INOP. THE L PACK; WHICH PROVIDES CONDITIONED AIR TO THE COCKPIT; WAS INOP AND AIRFLOW PROVIDED BY THE OPERATIVE R PACK TO THE COCKPIT WAS MINIMAL. GIVEN THE FACT THAT DEP ARPT GND TEMP WAS 34 DEGS C; NO CONDITIONED AIR CART WAS PLANNED FOR NOR PROVIDED AT THE GATE. OUR NORMAL GND TIME IS 30 MINS; BUT AN ADDITIONAL 20 MIN DELAY OCCURRED DUE TO ACTUAL FUEL LOAD BEING 1000 LBS LESS THAN OUR RELEASE. CABIN TEMP AT TIME OF PUSHBACK/TKOF WAS 99 DEGS F WITH COCKPIT TEMP ESTIMATED AT 10-15 DEGS HIGHER -- 1 OPERABLE AIR-CONDITIONING PACK WILL NOT COOL THE CABIN NOR COCKPIT ADEQUATELY IN THIS CONDITION. AT THE TIME OF THE INCIDENT; ESTIMATED COCKPIT TEMP WAS MINIMUM 90 DEGS F WITH VIRTUALLY NO AIRFLOW AND WE WERE MISERABLE. OVERALL STRESS LEVELS INCREASED WHILE THE MENTAL AND PHYSICAL WELL-BEING OF THE FLT DECK CREW SLOWLY DETERIORATED (INCREASING TIREDNESS AND IRRITABILITY WERE PRIMARY SYMPTOMS). UNDER THE ENVIRONMENTAL CONDITIONS WE WERE SUBJECTED TO; IT DIDN'T TAKE LONG TO DETERMINE THAT PLT INCAPACITATION COULD BE A SERIOUS OUTCOME BASED ON INDIVIDUAL TOLERANCE TO THE HEAT. CHAIN OF EVENTS ULTIMATELY LED TO THIS ALTDEV. HINDSIGHT BEING 20/20; COULD HAVE BEEN BETTER NOT TO DISPATCH THIS ACFT DURING THE HEAT OF THE SUMMER DAY.