A321 CAPTAIN REPORTS OVERHEATED ACFT; DELAYED MAINT; INABILITY TO CONTACT DISPATCH IN A TIMELY FASHION AND A FAILURE TO COMPLY WITH ALT RESTRICTIONS RESULTING FROM A PACK DEFERRED INOPERATIVE.

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WE WERE DISPATCHED WITH THE #1 PACK INOP ON MEL. DURING CLB TO OUR CRUISE ALT; WE ACCEPTED A CLRNC TO CLB TO AND MAINTAIN FL340. AFTER CRUISING AT FL340 FOR SEVERAL MINS; WE REALIZED THAT WE SHOULD NOT HAVE ACCEPTED THE CLRNC TO FL340; AS THE MEL FOR SINGLE PACK OP LIMITS THE CRUISING ALT TO FL310. SINCE WE WERE NWBOUND; WE SHOULD HAVE REQUESTED A FINAL CRUISING ALT OF FL300. I BELIEVE THE REASON WE DIDN'T CATCH THIS MISTAKE SOONER WAS THAT WE WERE NOT AS ALERT AS WE SHOULD HAVE BEEN DUE TO AN EXHAUSTING AND VERY TRYING 2 HR MECHANICAL DELAY ON THE GND PRIOR TO THIS FLT. THE PROB BEGAN IN ZZZ WITH A SINGLE-ENG TAXI OUT TO THE RWY WHERE WE HAD A PACK OVERHEAT AND TRIP OFF. (THE PACK OUTPUT HAD REGISTERED 100 DEGS C ON THE ECAM.) THE CABIN HAD ALREADY BEEN VERY WARM BEFORE WE LEFT THE GATE DUE TO INADEQUATE COOLING FROM THE GND AIR CONDITIONING UNIT. OAT WAS 111 DEGS. WHILE WE WERE WORKING ON THE PROB; THE CABIN BECAME EVEN WARMER. WE COULD NOT RESOLVE THE PROB AND TRIED TO CONTACT MAINT CTL AND SECURITY CTL THROUGH ACARS. AFTER NOT HAVING RECEIVED A RESPONSE; WE TRIED CONTACTING ZZZ MAINT BY RADIO AND THEY WERE UNABLE TO BE OF MUCH HELP; EXCEPT TO ADVISE WE COULD OPERATE WITH A SINGLE UNDER PROVISIONS OF THE MEL. SINCE OUR CRUISE ALT WOULD BE LOWER THAN PLANNED; WE WANTED TO CONTACT DISPATCH TO GET A NEW FUEL BURN AND TO MAKE SURE WE WOULD HAVE SUFFICIENT FUEL TO FLY SAFELY TO PDX. DURING THIS DELAY; THE CABIN TEMP CONTINUED TO CLB TO 94 DEGS TO 96 DEGS AND THE CABIN CREW RPTED MUCH PAX DISCOMFORT AND MANY COMPLAINTS. (THE COCKPIT WAS REGISTERING 100 DEGS.) AFTER NO RESPONSE TO NUMEROUS ATTEMPTS TO CONTACT DISPATCH BY ACARS; WE MADE THE DECISION TO RETURN TO THE GATE TO SORT THINGS OUT AND TRY TO COOL THE ACFT BACK DOWN TO A REASONABLE TEMP. AT THE GATE; MAINT BOARDED THE ACFT AND DECIDED TO MEL THE MALFUNCTIONING PACK. PAX HAD DEPLANED BECAUSE IT WAS SO UNCOMFORTABLE ON THE ACFT. ACFT HAD COOLED DOWN SOMEWHAT AND PAX BEGAN TO RE-BOARD. 'C' FLT ATTENDANT SAID HE WAS NOT FEELING WELL DUE TO THE HEAT AND WANTED TO BE REPLACED. HE WAS HAVING GREAT DIFFICULTY GETTING THROUGH TO CREW SCHEDULE; SO I OFFERED TO CALL AS WELL. I FIRST RADIOED ZZZ OPS TO ADVISE THEM OF THE PROB AND ASKED IF THEY COULD CONTACT CREW SCHEDULING. THEN I CALLED THEM MYSELF AND TALKED WITH A PLT SCHEDULER AND ASKED THAT THEY CONTACT A FLT ATTENDANT SCHEDULER. AFTER A LONG DELAY; THE REPLACEMENT FLT ATTENDANT BOARDED THE ACFT AND WE PUSHED BACK. AS WE CALLED GND CTL FOR TAXI CLRNC; ATC SAID THEY COULD NOT FIND OUR FLT PLAN; BUT WE COULD CONTINUE TO TAXI AND SHOULD CALL OUR DISPATCHER TO RE-FILE. AFTER NUMEROUS ACARS MESSAGES TO DISPATCH THE NEW FLT PLAN NEVER SHOWED UP. ACFT TEMP CONTINUED TO CLB WHILE WE WAITED AND ACARS'ED AGAIN TO ASK TO RE-FILE AGAIN. PAX WERE AGAIN COMPLAINING OF HEAT AS THE CABIN TEMP WAS BACK UP TO 94-96 DEGS AND THE COCKPIT WAS REGISTERING 100 DEGS. NOW WE WERE APCHING OUR MINIMUM FUEL FOR TKOF; SO WE ACARS'ED AGAIN TO GET THE RELEASE AMENDED. AFTER SOME DELAY; WE FINALLY RECEIVED OUR CLRNC AND RELEASE AMENDMENT AND CONTINUED TO TAXI TO THE RWY. WE TOOK OFF AND EVENTUALLY WERE CLRED TO FL340. WE WERE SO HOT AND DRAINED AT THAT POINT THAT WE FORGOT ABOUT THE FACT THAT WE WERE LIMITED TO A CRUISE ALT OF FL300. APPARENTLY THE DISPATCHER HAD ALSO FORGOTTEN ABOUT OUR LIMITATION WHEN RE-FILING OUR FLT PLAN. 1) WE HAVE HAD ONGOING PROBS IN GETTING TIMELY RESPONSES FROM DISPATCH AND MAINT WHEN USING ACARS. WE HAVE BEEN TOLD THAT DISPATCHERS ARE OFTEN UNAWARE THAT WE HAVE SENT THEM AN ACARS MESSAGE BECAUSE OF THE WAY OUR ACARS MESSAGES ARE DISPLAYED ON THEIR COMPUTER. THIS PROB MUST BE RESOLVED IMMEDIATELY. 2) IF A DISPATCHER OR MAINT CTLR IS BUSY WHEN THEY RECEIVE AN ACARS MESSAGE FROM US; THEY NEED TO REPLY WITH AN 'I'M WORKING ON IT' OR AN 'I'M BUSY RIGHT NOW AND WILL GET BACK WITH YOU SHORTLY' MESSAGE. NOT RESPONDING TO US IN A TIMELY MANNER IS UNACCEPTABLE. 3) THE GND AIR CONDITIONING UNITS ON THE JETWAYS IN ZZZ ARE INADEQUATE TO COOL THE ACFT WHEN IT IS HOT OUTSIDE. THIS OFTEN RESULTS IN VERY UNCOMFORTABLE AND IN SOME CASES UNSAFE CONDITIONS FOR OUR PAX AND CREWS. IT ALSO CONTRIBUTES TO MALFUNCTIONS AND FAILURES OF ACFT EQUIP. KEEPING ACFT COOL AT THE GATE HELPS US RUN A SAFE AND QUALITY OP AND WOULD RESULT IN LESS FUEL USAGE BY NOT HAVING TO RUN THE APU FOR COOLING. EVERYONE AND EVERYTHING WORKS BETTER WHEN THE TEMP IN THE ACFT IS COMFORTABLE.