B737-300 WAS DISPATCHED WITH BOTH APU AND 1 PACK INOP. CABIN BECAME UNCOMFORTABLY HOT BEFORE PUSHBACK.

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THE ACFT WAS DISPATCHED WITH AN INOP APU AND INOP R AIR CONDITIONING PACK. AS SOON AS I SAW THE RELEASE WITH THE 2 MELS MY RED FLAGS WENT UP. IT WAS ALMOST 90 DEGS AND WE HAD 137 PAX. I WAS CONCERNED THAT WE WOULD NOT ADEQUATELY BE ABLE TO COOL THE CABIN FOR THE PAX COMFORT (IT'S DIFFICULT WITH 2 PACKS OPERATING IN THE SUMMER ON B-300'S). MY ADDITIONAL CONCERN WAS THE INOP APU AND HAVING NO CTL ON THE REMAINING L PACK WHILE PARKED AT THE GATE. I WATCHED AS THE PAX WERE GETTING OFF THE FULL FLT (OUR INBOUND ACFT) AND THEY WERE SWEATING AND APPEARED VERY HOT. WE CARRY A LOT OF FRAGILE PAX AND I BEGAN TO THINK ABOUT OUR PAX'S SAFETY; AND WHAT I PERCEIVED TO BE AN IMPENDING PROB WITH PAX COMFORT AND SAFETY. I CALLED DISPATCH AND VOICED MY CONCERNS TO THE DISPATCHER; AND CHIEF PLT ON CALL. I WAS TOLD WE HAD NO SPARES IN ZZZ AND THE ACFT HAD BEEN SWAPPED TO A SHORT FLT (TO MITIGATE LENGTH OF TIME IN A WARM/HOT AIRPLANE); AND THAT THE FOLLOWING FLT (BACK TO ZZZ TO TERMINATE) ONLY HAD 29 PAX. I THANKED THEM FOR THE INFO AND PRESSED ON. MY FO TOLD THE RAMP NOT TO DISCONNECT GND AIR UNTIL THEY GOT A VERBAL FROM US ON THE RADIO. THE OPS AGENT CAME IN WITH THE LOAD SHEET AND SAID HE HAD RADIOED IN THE GALS ADDED (WE HADN'T EVEN BEEN REFUELED YET AND ALL THE PAX WERE ON THE ACFT). THE GND AIR WAS BLOWING WARM AIR THE ENTIRE TIME AND THE CABIN WAS GETTING REALLY HOT. THE NEXT THING I KNEW; THE OPS AGENT PULLED THE JETWAY BACK FROM THE ACFT (WITHOUT HIS COPY OF THE RELEASE); PULLED DOWN THE RETRACTABLE DOOR; AND LEFT. WE HAD JUST STARTED GETTING OUR 8000 LBS OF GAS. THEN ONE OF THE RAMPERS TURNED OFF THE GND AIR WITHOUT ASKING US. THERE WAS NO OPS AGENT; NO ONE ON FLT INTERPHONE (THE FORWARD AND AFT BINS WERE STILL OPEN); AND WE HAD NO AIR FLOWING TO THE PAX. THE RAMPERS COULDN'T GET THE GND AIR BACK ON. I'M LOOKING AT THE DOOR LIGHTS; GAS FLOWING; AND HOPING ANY SECOND WE WOULD HAVE EVERYTHING WRAPPED UP. THE ATTENDANT CALL SOUNDED AND THE B FLT ATTENDANT SAID A KID WAS FEELING ILL IN THE BACK BECAUSE IT WAS SO HOT. APPROX 7 MINS HAD ELAPSED WITHOUT ANY PRECONDITIONED AIR AND THE RAMP STILL WASN'T READY. I IMMEDIATELY CALLED OPS AND ASKED FOR AN OPS AGENT; PRECONDITIONED AIR; AND POSSIBLY THE DEPLANING OF THE PAX. ONCE THE JETWAY WAS BACK ON THE ACFT; I GOT UP; MADE A PA TO THE PAX APOLOGIZING FOR THE HOT CONDITIONS; AND TALKED TO THE OPS SUPVR THAT HAD COME DOWN THE JETWAY. I WAS PRETTY EXCITED AT THIS POINT AND AT FIRST WANTED TO PULL ALL THE PAX OFF THE ACFT BEFORE ANYONE HAD A HEAT RELATED MEDICAL INCIDENT. THE OPS SUPVR DIDN'T WANT TO PULL ANYONE OFF THE ACFT; UNLESS THEY HAD REQUESTED MEDICAL TREATMENT. I ASKED MY FO AND THE FLT ATTENDANTS TO PASS THROUGH THE CABIN AND ASSESS THE TEMP AND PAX. THEY CAME BACK AND SAID WITH THE GND AIR BLOWING AGAIN; THE CABIN TEMP WAS COMING DOWN. THE B FLT ATTENDANT SAID THE KID IN THE BACK WAS OK AND NO PAX HAD OR WERE REQUESTING MEDICAL TREATMENT. AT THIS POINT; WE HAD THE GAS; THE BINS WERE LOADED; THE ACFT WAS READY; AND THE CABIN HAD GOT SOME PC AIR FOR APPROX FIVE MINS; SO WE DEPARTED. THE FLT PROCEEDED UNEVENTFULLY. AT OUR ARR CITY; SOME OF THE PAX TOLD THE FLT ATTENDANTS THAT THIS WAS THE WORST EXPERIENCE THEY HAVE HAD FLYING AND THAT THE CABIN WAS TOO HOT THE ENTIRE TIME. WE COLLECTIVELY FAILED OUR CUSTOMERS BY OPERATING AN ACFT THAT HAD A R PACK AND AN APU INOP ON A HOT; HUMID SUMMER DAY. THE ACFT SHOULD HAVE BEEN LOOKED AT BY MAINT PREVIOUSLY IN THE FIRST CITY; OR UPON ARR AT ZZZ. I WOULD HOPE IN THE FUTURE WE WON'T BE DISPATCHING ACFT WITH A R PACK INOP AND AN APU INOP ON HOT SUMMER DAYS; ESPECIALLY IF THE ACFT IS IN A MAINT BASE. I THINK WE SHOULD MANDATE THAT AN ACFT WON'T BE DISPATCHED FOR PAX SVC WITH A R PACK INOP DURING THE SUMMER OR WINTER MONTHS. I ALSO THINK THAT WE SHOULD NEVER DISPATCH AN ACFT FOR PAX SVC WITH BOTH THE R PACK AND APU INOP.