Air carrier Captain reported an Air Pack Fault message during cruise and diverted to nearby airport.

Narrative

During cruise at FL370; AIR PACK 1+2 OVHT and (or just) AIR PACK 1+2 FAULT ECAM message. PACK 1 was on deferral under MEL 21-XX-XXX. Additionally Configuration Deviation List (CDL) XX-XX was utilized for both pack outlet flaps. Pack outlet temperature was high but barely in amber and only intermediately amber. Passengers and Flight Attendants were seated while we coordinated with ATC for a descent. Once Cabin Confirmed secured and while maintaining view of Outlet temperature; we began descent and initiated the ECAM generated depressurization. We donned oxygen masks and performed descent in accordance with the descent profile respecting weather conditions. At some point ATC [provided priority handling to us] on our behalf as we relayed our system issue. We were cleared to 10;000 feet and then to 7000 feet.Cabin Altitude reached 12;000 feet as we descended. Cabin oxygen masks did not deploy. We successfully diverted to ZZZ; [terminating the priority handling services] once level at 7000 feet. We were able to turn on PACK 2 once the overheat condition ceased around 4000 feet. Cabin temperature had reached 82 degrees. This plane had just the right factors for the Fault. We were mostly full with two deferred Outlet flaps and a deferred PACK. Maybe we should revisit the CDL and reconsider the suitability for the deferrals we were operating under. Also; we need to consider the cabin air filtration routine maintenance. We might benefit from more aggressive filtration replacements and inspections.