A319 Captain reported a hydraulic system malfunction during cruise flight that required a diversion to the nearest suitable airport.

Narrative

About 2 minutes after level off at FL320 we got an ECAM for the Hydraulic Reservoir Overheat. The system shut down and the Power Transfer Unit (PTU) inhibited. We canceled the Caution; I remained flying and I had the first Officer run the ECAM. The autopilot remained engaged. The ECAM gave us the option to recover the system if the overheat extinguished. It did after about 10-15 minutes and we recovered the system and then reviewed the Flight Manual (FM) for any additional info. We then contacted Dispatch and Maintenance Control for their recommendations. We all agreed that we could continue to ZZZ1; however I did say if the overheat returned we would return to ZZZ. All good. After about another 10-15 mins; the overheat ECAM returned. We got clearance to return to ZZZ; [requested priority handling] and then sent an ACARS message to Dispatch that we [requested priority handling] and were returning to ZZZ. We also requested that equipment be standing by and a tow vehicle if we had to land with the system out to tow us to the gate. I then transferred flying duties to the First Officer as I briefed the Purser and passengers. I gave the purser my briefing and not to prep for evac. I did tell her we may have to tow to the gate. Just prior to descent; the overheat condition stopped. We both agreed that we should leave the system off until we needed it for landing. We repowered it on the base leg and landed with full hydraulics. After landing; we cleared the runway and the commander requested that we stop for an exterior inspection. All was good and we taxied to the gate for a normal deplaning. I felt our training kicked in and was a great help. We communicated with all parties and got everyone on board for a safe return. Well done by all involved.