B737 FO LAMENTS MEL'ED APU ON HOT SUMMER DAY AS WELL AS POOR CHECKLIST USAGE AND DEPARTURE BRIEFINGS.

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FLT X WAS A LINE FERRY FLT FROM ZZZ TO ZZZ1 FOR REVENUE FLT Y (ZZZ1 TO ZZZ2). ON TAXI OUT FROM ZZZ WE HAD A L WING BODY OVERHEAT LIGHT ILLUMINATE. THE LIGHT REMAINED ON AFTER THE APPROPRIATE CHKLIST WAS ACCOMPLISHED. WE RETURNED TO THE GATE AND AN APPROX 4 HR DELAY ENSUED. MAINT FINALLY DISCOVERED THE APU BLEED WAS LEAKING HOT AIR NEAR THE TAIL SECTION OF THE ACFT. MAINT SAID THEY DIDN'T HAVE THE PART TO FIX IT AND THAT THEY COULD DEFER THE APU. I STRONGLY STATED; IN NO UNCERTAIN TERMS; TO THE MECH AND THE CAPT; I WAS NOT COMFORTABLE GOING TO ZZZ1 WITH THE APU DEFERRED. THE MECH SAID THE 3 BARS ON MY SHOULDER MEANT THAT MY OPINION DIDN'T COUNT. THE CAPT SAID IT WAS FINE WITH HIM TO GO IF ZZZ1 HAD A GND CART AND START CAPABILITY; WHICH HE SAID HE VERIFIED WITH DISPATCH. HE ALSO TOLD DISPATCH THAT HE WOULD TAKE IT ON THE CONDITION THAT THE AIRPLANE WOULD BE FIXED IN ZZZ2 WHERE THEY DID HAVE THE NECESSARY PART (VERIFIED BY THE MECH) TO WHICH THE DISPATCHER AND MECH SEEMED TO AGREE. OUTSIDE TEMP WAS APPROX 90 DEGS; AND THE ACFT WAS ALREADY HOT SITTING AT THE GATE (80+ CABIN; APPROX 90+ FLT DECK). DESPITE MY ADVOCATING FOR GETTING ANOTHER AIRPLANE; THE CAPT SAID HE WAS 'MISSION ORIENTED' AND THAT HE DIDN'T SEE A SAFETY ISSUE. HE MADE THE DECISION TO GO WITH THE PLANE WE HAD. I DIDN'T REFUSE TO FLY BECAUSE I DIDN'T WANT TO GET CALLED IN TO THE FLT OFFICE FOR REFUSING TO FLY WHEN A CAPT WITH MORE EXPERIENCE THOUGHT IT WAS SAFE. ON TAXI OUT; THE TEMP PROCEEDED TO INCREASE AND DIDN'T REALLY COOL OFF MUCH INFLT; PACK SUPPLY DUCT TEMP WOULD ONLY LOWER TO ABOUT 70 DEGS WITH BOTH PACKS AT FULL COLD IN 'AUTO.' USING 70 DEG AIR TO COOL A 90-PLUS DEG FLIGHT DECK WITH 3 AIR VENTS DOESN'T WORK WELL. WHEN WE ARRIVED IN ZZZ1; GND AIR WAS ATTACHED BUT WAS NOT WORKING; WHICH THE GND CREW APPARENTLY KNEW ABOUT. THE UNIT WAS BLOWING 90 DEG AIR AND ITS COMPRESSOR FANS (SEEN FROM THE FLT DECK) WERE WINDMILLING (INOP) AND THE STATION HAD NO AIR START CART. FIRST THEY BORROWED AN AIR START CART; ONE FROM ANOTHER AIRLINE (?) WHICH DIDN'T WORK; THEN THEY BORROWED ANOTHER WHICH WORKED FINE. BY NOW COCKPIT TEMP WAS 95-100 DEGS WITH AN UNKNOWN HUMIDITY (DEW POINT WAS IN THE 70'S; I BELIEVE); CABIN TEMP WAS BTWN 85-90 BY THE GAUGE (THE CABIN HAD COOLED TO ABOUT 75 DEGS INFLT). IT WASN'T UNTIL WE WERE IN THE AIR THAT I REALIZED HOW MESSED UP OUR DEP WAS. THE DEP BRIEF CONSISTED OF 'ARE YOU READY?' THE BEFORE PUSHBACK CHKLIST WAS ACCOMPLISHED AFTER WE HAD PUSHED 50 FT FROM THE GATE. ON TKOF/CLBOUT I HAD NO IDEA WHAT ACCELERATION HT WAS AND THOUGHT WHAT WERE WE THINKING? THE CAPT TURNED THE HDG BUG TO THE WRONG HDG AFTER TKOF (I DON'T KNOW WHERE THE HDG CAME FROM BUT IT TURNED OUT TO BE WITHIN 20 DEGS OR SO OF WHAT IT SHOULD HAVE BEEN). WHEN THE DEP CTLR ASSIGNED US THE APPROPRIATE HDG FOR THE RWY IN USE; I CHKED THE DEP PLATE AND YES; WE HAD BEEN ON THE WRONG ONE. THE CLB WAS NOT PROGRAMMED IN THE FMC SO THAT STEP HAD BEEN SKIPPED AS WELL. THIS MADE ME WONDER WHAT ELSE WASN'T PROGRAMMED SO I CHKED THE RTE WHICH THE CAPT ENTERED -- IT WAS CORRECT. ON THIS FLT; IT TOOK ABOUT 40 MINS FOR THE FLT DECK TO COOL TO A COMFORTABLE TEMP. ABOUT THAT TIME THE CAPT STATED 'NOW I'M RETHINKING MY DECISION TO TAKE THIS AIRPLANE IN ZZZ1. I THOUGHT 'NO KIDDING?' BUT SAID NOTHING; SINCE I THOUGHT I WAS PRETTY CLEAR BEFORE. ON ARR AT ZZZ2; ANOTHER CREW WAS WAITING TO TAKE THE PLANE TO ZZZ3. SO MUCH FOR MAINT TELLING US THEY WOULD FIX IT IN ZZZ2. SO MUCH FOR DISPATCH TELLING US ZZZ1 HAD GND CART. AS FAR AS I'M CONCERNED; THEY FLAT OUT LIED ABOUT IT ALL. I HAVE FLOWN WITH THIS CAPT BEFORE AND THINGS WERE BY SOP. THE ONLY EXPLANATION I HAVE FOR BOTH OUR LACK OF PERFORMANCE AND VIGILANCE WAS THE HIGH HEAT AND STRESS OF THE FLT DECK. IF THERE IS A NEXT TIME; I WILL TELL THE CAPT HE HAS THE AUTH TO ACCEPT THE ACFT; AND THAT I WILL CALL SCHEDULING TO LOOK FOR A NEW FO FOR HIM; I WILL REFUSE TO FLY. THESE UNSAFE SITUATIONS WERE 100% PREVENTABLE AND IF WE HAD ENCOUNTERED AN ENG FAILURE/FIRE/CRITICAL MAINT ISSUE; IT MIGHT NOT HAVE SEEMED AS UNEVENTFUL AS A 20 DEG HDG DEV.