Your CHT gauge and probe should be a Stewart Warner. The original Stewart Warner probe for your aircraft is PN S1372-1. The Ohms reading for the probe should be 310.0 at 220 degrees F and 34.8 at 450 degrees F. Paul Malkasian makes a test box to check the gauges themselves, (CHT, fuel and Oil temp) http://www.fuelsenders.com/site/898219/product/MGTB1.
Be sure and check the wiring on the back of the gauge and make sure that there isn’t any corrosion on the terminals or loose wires.
If you do find that the gauge is bad, Paul Malkasian at Instrument Rebuild in Sequim, WA 360/683-6245 or his web site www.fuelsenders.com can repair them.
If you find that the probe is bad, they are no longer available and Cessna switched to Rochester. Unfortunately the Stewart Warner gauges are not compatible with the Rochester probes and vice versa. The superseded PN for the original probe is a Rochester probe. One option is to take the new probe (Rochester) and send the probe and gauge off to Instrument Rebuild in Sequim, WA (360/683-6245) and have the Stewart Warner gauge calibrated to the new probe.