You're listing symptoms that I can't tell for sure if they're related or not, so I think the best place to start is by finding a scanner, or a mechanic with one, to view live data and see exactly what the Engine Computer is seeing. If the computer is seeing normal operating temperatures, but they're varying up and down at first, particularly for the first ten minutes after starting the engine, you may benefit from adding a tiny bypass hole to the thermostat.
Most import engines have a thermostat with a very small bleed hole in them. Domestic engines typically don't. I replaced the thermostat in my '88 Grand Caravan many years ago with one that didn't have the bleed hole. The temperature gauge worked fine for many years after that, but one day I noticed the coolant temperature came up really fast, went too high, then suddenly dropped to too cold, then repeated. That cycle repeated four or five times before it stabilized and read normally.
What happened was the temperature sensor for the dash gauge was some distance away from the thermostat. High temperature would show up at the sending unit and be reported as overheating first, then the high temperature would slowly migrate to the thermostat causing it to open. Once it opened, the cold coolant from the radiator would rush in and cause the gauge to go down and the thermostat to close.
The purpose of the bleed hole is to allow the hot coolant to flow to the thermostat right away. I drilled a 1/16" hole in mine and never saw that problem again in over 150,000 miles.
During the '90s, most cars used two separate coolant temperature sensors. The single-wire sensor was for the dash gauge and the two-wire sensor was for the Engine Computer. If the scanner shows coolant temperature is varying wildly like the dash gauge shows, consider adding that bleed hole. If the temperature is holding steady, we may have an instrument cluster problem and the oil gauge is providing another clue.
Coolant temperature sensors have an extremely low failure rate, so look for other causes first. Also, dash gauges are notoriously inaccurate. They are best used for the driver to observe when something is out-of-the-ordinary, never for exact temperature.
Thursday, October 6th, 2016 AT 3:25 PM