Air carrier flight crew reported pressurization pack failure during departure climb. Returned to departure airport.

Narrative

Normal taxi out and takeoff with single pack operation (#2). Climbing thru 8;000 ft we received an ECAM advisory for #2 pack high inlet temp. Inlet temp was indicating 105 and pack flow indicating arrow was showing full scale deflections from high to low. We referred to ECAM advisory checklist in QRH; unable to compare pack flows or switch packs as #1 pack was already deferred. We tried adjusting temperature selection to a warmer setting in the event the pack was freezing up. During this process we continued climbing to cruise altitude of 31;000. The higher altitude and various pack temp selections did not lower the inlet temp on pack. Previous to this I had notified Dispatcher we were having difficulty with #2 pack. There was a delay from Dispatcher response. I asked about a possible divert and a destination. There was a delay to response and #2 pack then became unusable. We were approximately 120 miles from ZZZ @ 31;000 ft. I made the decision to return to ZZZ and use the deferred #1 pack. We notified ATC and I sent message to Dispatcher that we were returning to ZZZ as [priority] aircraft. In prior discussions with Maintenance in both ZZZ2 and ZZZ they believed the #2 pack was unreliable with low airflow. I [advised ATC] for a quick descent and the fact that I was using a deferred system. The #1 pack worked normally without any warnings. Around 80 miles and at 10;000ft MSL we received another message from Dispatcher asking us if we could divert to ZZZ1. I did not feel comfortable changing destinations again while using a deferred pack which had a slowly rising inlet temp as well. The approach and landing were normal and I did not request any special equipment for landing. After shutdown I entered the pack failure into logbook but did not enter the note air turn back on log page.