FLT CREW OF A320 CLBED TO FL350 DURING TSTM DEV CONTRARY TO DISPATCH MEL LIMITATION TO FL310 DUE TO AN INOP PACK.

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AS A RESULT OF THE MECHANICAL; WE WERE DISPATCHED WITH A SINGLE PACK OPERATIVE AND WERE LIMITED TO FL310 OR LOWER. WE WERE PREVIOUSLY FILED TO FL350. ON DEP; WE WERE DISTR BY TSTMS IN THE AREA AND ACCEPTED A CLRNC TO FL350 AND CLBED TO FL350. AFTER ABOUT 20 MINS AT THAT ALT AND WHEN WE WERE CLR OF THE TSTMS; THEN WE REALIZED WE HAD CLBED TO FL350 WHEN WE HAD INTENDED TO GO NO HIGHER THAN FL310 DUE TO THE SYS PROB. WE IMMEDIATELY REQUESTED AND DSNDED TO FL310. THE FLT CONTINUED TO MCO WITH NO FURTHER PROBS. I BELIEVE THE EXCEEDANCE WAS DUE TO A COMBINATION OF CREW FATIGUE AND THE WX. I REMEMBER WHEN WE WERE CLRED TO FL350 THINKING THAT WOULD AID IN OUR DEVS AROUND WX. I FORGOT ABOUT THE EXISTING ACFT SYS PROB DUE TO BEING TIRED AS WELL AS CONCERNED ABOUT WX AVOIDANCE. IN THE FUTURE; I WILL PLAN ON UPDATING MY CLRNC OR HAVE DISPATCH UPDATE IT WITH ATC PRIOR TO DEP. SUPPLEMENTAL INFO FROM ACN 586887: MAINT CALLED TO DEFER THE #1 PACK INOP AT DEP TIME. I HAD STEPPED AWAY FROM MY DESK FOR A MOMENT AND ANOTHER DISPATCHER ANSWERED THE CALL FOR ME. WHEN I RETURNED TO MY DESK; THE OTHER DISPATCHER ASKED IF I WAS AGREEABLE TO DEFER THE PACK INOP AND I SAID I WAS. HE SAID HE WOULD SEND THE RELEASE FOR ME AS HE ALREADY HAD IT SET UP ON HIS COMPUTER. I CHKED AND SAW THAT THE NEW RELEASE HAD BEEN SENT AT FL310; BUT I FAILED TO CONFIRM IF HE HAD REFILED THE FLT PLAN WITH ATC (HE HAD NOT).