I have 2009 Cobalt that we have tried about everything to fix in the coolant system. The digital gauge reads up to 260 but when you put the gun on the different parts they read nominal temperatures. Replaced the thermostat, water pump, radiator, and temperature sending unit, but the digital read out still shows high.
Have you tried cleaning the ECM connector? If it cures the bad reading add dielectric grease to the pins of the connector to attempt preventing water from getting in.
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You may also need to re-seat the connectors under the fuse block under the hood.
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