C550 pilot reported aircraft oil temperature issues and returned to departure airport.

Narrative

I departed ZZZ at approximately XA:30 PDT in Aircraft X on a flight to ZZZ1. Normal preflight was performed and take-off was normal. Departed on Runway XX and flew the ZZZZZ4 departure. Initial climb out was normal. At approximately 10000 MSL; I noticed the #2 oil temperature tape was considerably higher than #1. It continued to climb and I asked ATC for a level off at 13000 to check the problem. They approved and I leveled at 13000 MSL. At this time; the oil temp gauge was approaching red line so I retarded the throttle on #2 engine. It made no difference and I decided to shut #2 engine down completely as it was continuing to climb. I [requested priority handling] with ATC and advised what I had done and requested to return to ZZZ. They vectored me back toward the airport and asked if I wanted equipment standing by. I told them let's change it to a precautionary shutdown of #2 engine and I did not need any equipment standing by. I told them I was doing fine and just needed to return to the airport. My intent was to let them know I was not in an priority situation but just a return to the field with a precautionary shutdown. I made a normal visual approach to Runway XX and taxied back to the FBO. I called the owner and have a mechanic from Company who is going to meet me at the airplane tomorrow and try and see what caused this. ATC did an excellent job and I appreciate their help and professionalism.