SR22 pilot reported engine roughness and loss of power resulted a request for priority handling and a diversion to make a precautionary landing.

Narrative

On Day 1; Aircraft X; a Cirrus SR22T Serial XXXX; received a yellow CHT CAS alert; all cylinders approaching 420 degrees; and the engine coughing and spurting with some surge. Unable to smooth the engine out; the pilot requested priority handling. Following are the pilot's comments: 'I had just reached a cruising altitude of FL160 and had not yet adjusted power or mixture following a normal climb. Upon reaching FL160; I received a yellow CHT CAS and all cylinders at or approaching 4XX degrees. I immediately pulled the power back to about 50%. The engine was coughing and spurting with some surge. I leaned the mixture out to cool CHTs; and they all responded and fell as expected. The engine was still surging and spluttering; so I requested priority handling; diverted to ZZZ; and then made a conscious call to leave power and mixture setting as is as I had partial power; which with the altitude; had sufficient performance to reach ZZZ. I was cleared down to 13;000 ft.; called the airport in sight and was cleared for a visual approach. The winds were calm; so I elected a right downwind for Runway XX; purposely remaining high until established on the long final. I then reduced power when I knew I had enough altitude for zero power glide and slipped down pretty aggressively for a standard full flap landing. Normal landing and taxied off Runway to FBO. The engine was still spluttering on the taxi--normal shutdown and tie-down.' The Cirrus Field Service was notified and asked the pilot for more information. Following are the pilot's reply to Cirrus Field Service: 'The fuel pump was on--the mixture in the green arc for the climb. Power reduced as per checklist. The mixture was leaned to cool CHTs which they responded. The initial pull is likely what you saw in engine data with low fuel flow; as the mixture lever seems more sensitive than other SR22Ts but quickly corrected to around 16--x FF. Mixture and power were left in place; as was the boost pump for the remainder of the flight. Again; I thought having a rough engine better than no engine; so I left everything in place to keep it stable--rough spluttering engine most of the way down and then again taxing after landing. It did feel like vapor lock behavior; although my experience with vapor lock is that it clears pretty quickly. So that's what I thought it was at first; but when it continued; I [requested priority handling.]