Experimental aircraft pilot reported that during departure an engine cylinder temperature became hotter than normal and the engine began to shake. Pilot executed an off-airport landing.

Narrative

I had an uneventful flight from ZZZ1 to ZZZ.The same day I departed ZZZ at approximately XA:30pm.With 4 hours of fuel on board I had 2+hrs of reserve.The departure was uneventful.  I climbed at full throttle 2;500 RPM.Just a couple of minutes after departure I noticed #2 engine cylinder temperature getting hotter than normal.I immediately reduced power to 2;200RPM and lowered my climb angle into a slight descent for better engine cooling.  Within 30 seconds all cylinder temps dropped-- except that one stubborn #2 cylinder. Its temperature lowered; but not to its normal operating temperature.  This problem cylinder was still high (400°F).I further reduced power to 2;000 RPM.  The hot cylinder #2 temperature dropped but; did not fully return to normal.  It remained high.After 30 seconds of normal operation I decided it was time to increase power and attempt another climb.As soon as I began advancing throttle RPM the engine made a hard shutter; then an aggressive out-of-balance type shaking.  I immediately reduced throttle setting to idle power.  The engine was still turning the prop but the engine was way out of balance like it would die any moment.  A few attempts moving the throttle lever did nothing to improve engine performance.Too low to reach the nearest airport; ZZZ2; I transmitted my mayday radio call on the ZZZ2 CTAF.  No answer.  At this point my workload was too pressing to call again. I chose to land off airport.I landed without incident. No damage to anyone; vehicles; nor property.FindingsContinental O-200#1 connecting rod seized and broke. (Front half of upper case had no evidence oiling.)#1 connecting rod broken piece bounced around inside case; damaging many components.