CE-172 pilot reported loss of engine power during cruise. Pilot diverted and was unable to reach an airport so landed off-field.

Narrative

Normal preflight and run-up. Normal T/O from ZZZ and climb out. Contacted ZZZ Approach for VFR flight follow to the freeway. Climbed to 3000 ft. msl and began cruise phase. Approximately 30 miles southwest of ZZZ1; loss of engine power occurred. I trimmed for best glide and began attempts to discover cause. I [requested priority handling with] ATC. They gave me initial headings to small private airstrip. The engine became rougher and began to shudder and backfire. Cylinder monitor showed two cylinders (I think it was 3 and 4 cylinder)an extreme red (temp) indication. I tried adjusting mixture; throttle; and checked both magnetoes; ignition and master switch. All were correct. I didn't try carb heat; because by that time my altitude was reaching critical height for landing. Engine continued running roughly; shaking and backfiring. I notified approach that I didn't have the airstrip in site and I was putting the plane into a field. Plane landed in a muddy plowed farmer's field. Once the plane settled; the front wheel caught causing a prop strike in the mud and the plane titled approximately 40 degrees; but settled back to level position. No injuries to PIC or passenger an no apparent exterior damage to aircraft.I have no idea what caused the loss of power; but the FBO's A and P [mechanic] noted from downloaded insturment data that the cylinders mentioned earlier were running temps in the 1800 degree F range.Contributing factors...unknownFactors affecting quality of human performance...noneActions/inactions...see above