SR20 pilot reported an engine malfunction during cruise flight on a IFR clearance. The pilot diverted to the departure airport and landed safely.

Narrative

All normal preflight and run-up checklist items were completed. I took off ZZZ runway XX southwest departure towards ZZZ1 did a touch-and-go departed runway XY to the SE where I picked up my IFR with approach. During cruise I was leveled out at 11;000 just south of ZZZ2 when a CHT yellow warning came on. I acknowledged the message and grabbed my QRH checklist; the message immediately went to red CHT warning. I ran the checklist explaining to center my issue and requested vectors back to ZZZ; they asked if I needed any assistance or if I was declaring an emergency I said no; I will advise if I require additional assistance. They transferred me to approach and vectored me around. Once I completed the checklist; I disengaged AP to gain airspeed and see if the red annunciator would turn off. The red annunciator kept flashing red. And eventually; a Yellow X indicator on CHT 2 came on and would not turn off after I ran the checklist. Because the power had to be reduced the plane had difficulty maintaining airspeed and altitude while in level flight; the engine ran a little rough but the engine was still running. Approach asked how many cylinders does my airplane have and the type of aircraft including souls on board while I was being vectored back. I informed them it was a Cirrus SR20 1 soul on board. Approach cleared me for the visual runway X into ZZZ and informed me that ZZZ tower was [requesting priority handling] for me. Landed safely with no further incidents and spoke to maintenance about the indicators and what happened; they said it was a good idea to land as soon as possible.