Don't know your 3.1 engine, but most temp sensors operate much the same way. There are much like bridge circuits where one of the resisters is placed somewhere in the cooling circuit where it's subjected to changes in the temperature of coolant and it responds with a change in it's resistance which then unbalances the bridge and this results in current flow thru the meter. A change like your reporting is probably not thermostat related but sensor related. There may be a bad connection at the sensor. I would be inclined to start at the sensor, even maybe changing it. Check for corrosion at the connection and assure all grounds are clean and connected.