AFTER CONFERENCE WITH DISPATCH AND MAINT COORD; AN ILLEGAL MEL ADJUSTMENT IS MADE BY A B737-300 FLT CREW TO A L WING BODY OVERHEAT INDICATION PRIOR TO DEP.

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WE PUSHED BACK FROM GATE. AFTER COMPLETING THE AFTER START FLOW AND JUST BEFORE CALLING FOR THE BEFORE TAXI CHKLIST; WE EXPERIENCED A L WING BODY OVERHEAT INDICATION. I CALLED FOR THE CHKLIST FOR THE L WING BODY OVERHEAT; WHICH THE FO COMPLETED. SOMEHOW IN THE PROCESS; WE COMPLETELY MISSED NOTE #5 IN THE QRH AND ENDED UP ON NOTE #6 THINKING WE COULD DISPATCH. WE THEN COMPLETED THE BEFORE TAXI CHKLIST AND TAXIED CLR OF THE RAMP AREA TO A SPOT WHERE WE COULD HOLD WITHOUT BLOCKING TFC. I THEN DIRECTED MY FO TO CONTACT DISPATCH VIA ACARS. I LOOKED AT MEL 26 CONCERNING THE L WING BODY OVERHEAT. I FAILED TO RECOGNIZE THAT MEL 26-12 IS FOR A FAILED WARNING SYS. IN MY MIND; I THOUGHT WE WERE COMPLYING WITH THE INTENT OF THE MEL AND THAT WE WERE GOOD TO GO. THE ACARS WAS SLOW; SO I CONTACTED DISPATCH BY COMPANY RADIO AND WAS GIVEN A RELEASE PER MEL 26-12. AFTER TKOF; WE GOT AN ACARS MESSAGE FROM DISPATCH TO RETURN TO THE GATE. WE SENT A MESSAGE BACK THAT WE WERE AIRBORNE AND THEN RECEIVED A MESSAGE BACK TO DISREGARD THE RETURN TO GATE MESSAGE. IN OUR NEXT CITY; I CONTACTED DISPATCH TO FINISH PROCESSING THE ACFT LOGBOOK AND MEL 26-12. AFTER REVIEW WITH DISPATCH AND MAINT; MY ERROR BECAME APPARENT AND CLR. IN CONCLUSION: CONSIDERING THAT THERE WERE 4 OR 5 PEOPLE INVOLVED IN THIS EVENT THAT MISSED NOTE #5 REQUIRING A RETURN TO THE GATE; POSSIBLY THE QRH AND/OR THE MEL COULD BE WORDED DIFFERENTLY. SUPPLEMENTAL INFO FROM ACN 616580: USING THE TECHNOLOGY OF ACARS; WE COMMUNICATED OUR SIT WITH DISPATCH. THE PROCESS WAS QUITE TIME CONSUMING AS WE PUNCHED OUT MULTIPLE MESSAGES AND WAITED FOR A RESPONSE. THE CAPT FINALLY JUST CONTACTED DISPATCH VIA THE RADIO. AT INITIAL RADIO CONTACT; DISPATCH HAD FINISHED CONSULTING WITH MAINT AND HAD AN MEL FOR US TO CONTINUE OP. WE MADE PROPER NOTATION AND PROCEEDED TO RWY 25R. ON DEP; WE HAD A FAILURE OF THE AUTO PRESSURIZATION SYS AND COMPLETED THE AUTO FAIL CHKLIST. THE PRESSURIZATION WAS WORKING NORMALLY IN THE STANDBY MODE UNTIL DSCNT INTO ZZZ1. AT APPROX 9000 FT; THE CABIN PRESSURE BEGAN TO CLB RAPIDLY TO 7000 FT AND WE WENT TO MANUAL MODE TO CORRECT THE PRESSURE. AT THE GATE; THE CAPT CALLED MAINT ON THE PHONE. MAINT NOW SAID THE MEL THEY GAVE US TO OPERATE UNDER DID NOT ADDRESS OUR SPECIFIC PROB. I BELIEVE THE CAUSE OF THIS ERRANT MEL WAS SIMPLE COM. WHILE THE ACARS IS NICE; IT IS DIFFICULT TO CONVEY DETAILED PROBS WITH ACCURACY AND COMPLETE COMPREHENSION BY BOTH PARTIES. IN THE FUTURE; IF THE SIT REQUIRES MORE THAN SIMPLE DIALOG; THEN I WILL COMMUNICATE WITH DISPATCH OR MAINT VIA RADIO. I WILL ALSO SCRUTINIZE AN MEL RECEIVED FROM DISPATCH OR MAINT TO VERIFY IT IS THE PROPER ONE.