AN ATR72 ON PREFLT CHK WAS FOUND TO HAVE THE R ENG BLEED VALVE INOP. THE CREW ELECTED TO TAKE THE ACFT BUT WERE UNABLE TO COOL THE CABIN INFLT RESULTING IN SICK PAX AND A CANCELED TRIP.

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WE WERE ON THE LAST ROUND TRIP OF A 3 DAY SEQUENCE. OUR ACFT ARRIVED FROM THE MAINT HANGAR AT DEP TIME. WE WERE TIRED AND READY TO GET THE LAST TRIP OVER WITH. THE ACFT WAS HEAT SOAKED AND WE BEGAN BOARDING A FULL LOAD OF PEOPLE. WE STARTED THE R ENG TO GET SOME AIR FLOWING THROUGH THE CABIN. AFTER A FEW MINS THE R ENG BLEED FAULTED WHICH HAS HAPPENED BEFORE WHEN IT IS VERY HOT. I BROUGHT THE PROP OUT OF FEATHER TO GET AIR FLOWING AROUND THE COWLING THINKING IT MIGHT ENABLE US TO RESET THE BLEED VALVE. IT RESET AND FAULTED AGAIN IN A FEW MINS. THOUGHT IT MIGHT COOL AND RESET WHEN AIRBORNE SO WE DEPARTED NOT WANTING TO DELAY. IT RESET IN THE AIR FOR A FEW MINS AND FAULTED AGAIN. CABIN TEMP 100 DEGS; SOME PAX AND 1 FLT ATTENDANT FELT SICK. ACFT GNDED IN MAF UPON ARR FOR ENG BLEED FAULT -- R ENG. I SHOULD NOT HAVE PUT 64 PEOPLE ON A HEAT SOAKED ACFT; AND DEPARTED WITH A MECHANICAL PROB. THIS RESULTED IN DANGEROUS CABIN TEMPS; FLYING AN ACFT WITH A KNOWN MECHANICAL PROB; AND HAVING TO GND AN ACFT AT AN OUT-STATION. IN OTHER WORDS; USING POOR JUDGEMENT -- IN AN EFFORT TO FINISH A TRIP. ONCE ENRTE I TRIED TO COOL THE CABIN BY USING THE R AIR- CONDITIONING PACK AND THE GND XFEED SYS WHICH IS A VIOLATION OF OUR PROCS. WHEN THE BLEED FAULTS THE ASSOCIATED PACK SHOULD BE OFF.