A B757 WITH A SINGLE PACK DEPARTED A HOT ARPT WITH A CABIN TEMP NEAR 100 DEGS AT TKOF. THE ACFT COOLED TO 80 DEGS IN FLT LEAVING THE CREW EXHAUSTED AND DEHYDRATED.

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THE R AIR CONDITIONING PACK WAS DEFERRED AFTER EXTENSIVE WORK BY MAINT. WE COULD NOT COOL THE CABIN USING PRECONDITIONED GND AIR OR APU AIR THROUGH THE OPERATING L PACK. A MECH AND LEAD CAME TO THE ACFT AND THE LEAD INSISTED THAT THE L PACK WAS OPERATING NORMALLY. HE STATED THAT IT AND THE RECIRCULATION FANS WOULD COOL THE CABIN ONLY AFTER THE ENTRY DOORS WERE ALL CLOSED AND THE ENGS STARTED. I ACCEPTED HIS EXPLANATION AND WE DEPARTED. WHILE WE TAXIED; THE CABIN GOT HOTTER; REACHING 100 DEGS F WHEN WE BEGAN OUR TKOF ROLL. IT TOOK 45 MINS OF FLT FOR THE TEMP TO COOL TO 80 DEGS F; AND WHEN WE INITIATED DSCNT THE TEMP BEGAN TO CLB RAPIDLY. THE INTERIOR WAS SO HOT DURING THIS FLT THAT MY FO AND I BOTH NOTED THAT OUR ABILITIES WERE BECOMING IMPAIRED AND THAT WE WERE MAKING PROCEDURAL ERRORS. AFTER WE BLOCKED IN AND DEPLANED; THE FLT ATTENDANTS TOLD US THAT MANY OF THE PAX HAD BECOME ILL AND THAT THE FLT ATTENDANTS THEMSELVES HAD IMPAIRED ABILITY TO FUNCTION DURING THIS FLT. HAD THE FLT ATTENDANTS DESCRIBED TO ME THE CONDITIONS IN THE CABIN PRIOR TO OUR TKOF; I WOULD HAVE RETURNED TO THE GATE AND REFUSED THE AIRPLANE. I BELIEVE THAT THIS LEAD MECH MISLED ME IN ORDER TO 'MOVE' THIS AIRPLANE; RESULTING IN A FLT THAT WAS NOT ONLY A GREAT DISSERVICE TO OUR CUSTOMERS BUT ALSO PRESENTED A SAFETY HAZARD TO THEM AND TO THE WORKING CREW.