Pilot reported one cylinder began to over heat during cruise. The pilot requested priority handling and diverted to make a precautionary landing.

Narrative

With 45 min of flight left and on an IFR plan with ZZZ Center; I was at 10;000 ft. The caution CAS message 'CHT' popped up with the warning for a cylinder heating up. It was in the yellow when the message first popped up; and it was cylinder 2. I pulled up the alert and immediately enriched the mixture to help cool the cylinder and switched tanks leaving the electrical fuel pump on. It helped momentarily and then the CAS message returned and quickly went from a caution message to a warning message in the red; the cylinder temperature was in the red zone. I went full rich and slightly pulled back power. It helped only for seconds. I asked ATC to descend because it looked like my cylinder was overheating. They asked me if it was an urgent situation; I replied 'not yet but I do need to land as soon as practicable' They gave me a 1;000 ft. and the Warning went away as I descended; once I leveled out it came back. I pulled the QRH out and ran through all the items. I proceeded to the last item; once I saw I had down the rest of the checklist... 'if warning annunciation remains illuminated; a. Land as soon as possible'. I asked ATC to divert to ZZZ1 and they vectored me over and around the terrain. I lost communications with them briefly and a [Company] flight relayed our messages to each other. I finally finished with them and they gave me the UNICOM for ZZZ. During my descent I did notice the CHT fluctuating in the green zone going up and down. I was functioning at 57% or less PWR on the descent. I did a straight in on Runway XX; landed and taxied off to parking. Once I stopped I called Maintenance and spoke with Person A that evening. He said he would call Person B and escalate the situation. Once he called me back he said that 'The asset could not be picked up until tomorrow morning' and he wasn't sure if anyone would be able to come pick me up. He then said that Person A said if I felt comfortable; I could fly the plane back. (ZZZ1 is not an easy airport to fly out of in the day let alone a night with no visual of all the terrain around). I had called Person C in Dispatch before the second conversation and he found an Instructor to come pick me up. Person A asked me to write the squawk in and allowed me to keep the plane running for heat since the temperatures were so low. I waited for a few hours before I got rescued. SO THANKFUL TO HAVE BEEN PICKED UP!I followed SOPs and expected SOPs to be followed after my landing. I couldn't believe that they inferred to fly a plane that if I would have landed in ZZZ2 would have been squawked and not allowed to be taken up until looked at by Maintenance. I do understand that there are many censor issues with the SR-20; but I am not qualified to make that call and an over the phone call doesn't seem sufficient to have a new pilot fly it without verifying if something is actually wrong. I don't believe it wise; even from a legal perspective to hint or ask someone if they feel comfortable flying an aircraft that had an issue even after checklists were ran and the problem persisted. There could have been something severely wrong and someone who is a people pleaser or wouldn't want to make waves; might have accepted the flight and with the forested and mountainous area around could have made that an even more dangerous flight out.