A320 Captain reported that on climb-out; there was a temperature exceedance in the engine #1 EGT with a fuel flow of 800 lb. over what engine #2 was showing. Upon landing; a message showed a possible FADEC error.

Narrative

Some background information - we showed up at the aircraft at XA:45 local time. The thrust reverser on the #2 engine was under MEL. During the engine #2 start we had an ignition fault that aborted the start. Contacted Dispatch and Maintenance before attempting a second start. The second start was successful. Then we had a #1 FD situation that also required us to contact Maintenance. Once that resolved we had to amend our release due to our fuel being below our planned minimum takeoff fuel. At that point of the flight; my First Officer and I were ready for anything to happen next.Due to the wet runway; we were going to do a TOGA takeoff with ZZZZ as a diversion field in case of problems. Around 800 ft. we got an ECAM indicating an exceedance engine #1 EGT of 650 [degrees] with a fuel flow 800 lb. over what engine #2 was showing. The thrust was decreased for the climb; bringing the EGT just below the max limit. Within 30 seconds; the EGT and the fuel flow started increasing again past the max limit. Being out of the overcast weather and still in the valley; we asked for a heading and leveled off at 8000 ft. and slowed to keep the EGT below the limit. Running the QRH and watching the way the EGT was moving; we realized that we had lost our ability to climb without running the risk of having to shut down the engine. Contacted Dispatch; explaining what was happening. We all agreed to make a precautionary landing in ZZZZ. Due to our reduced power settings we were able to keep EGT below the limit and therefore; stay out of the QRH. While flying towards ZZZZ we received a message from Dispatch asking us if we had declared an emergency. At this time I had not declared yet. ZZZZ Tower started acting as if we had declared; asking us for SOB and fuel - they even conducted a runway inspection after we landed! I got busy reviewing our fuel and weight situation and did not get a chance to readdress the need to declare. Still being below 10000 ft. at night with possibly an engine we may have to shut down; I decided that an overweight landing was safer than holding to burn fuel. We ran the QRH for an overweight landing and briefed the inflight crew members; as well as the passengers. Shortly after touchdown we had a #1 Engine Compressor Vane Fault message indicating a possible FADEC (Full Authority Digital Electronic Control) failure. Taxied to the gate at ZZZZ using power from #2 engine as per QRH. Aircraft was put out of service upon arrival.