Temperature gauge and heater/AC fan fluctuating up and down

Welcome to 2CarPros.

That sounds like a voltage issue. What I need you to do is check battery voltage when this is happening. See what the voltage at the battery is when the problem is happening and see if it is fluctuating. If it is, there may be an issue with either the alternator or the voltage regulator (which is internal on the PCM). I will explain that if needed.

Here is a link that shows how to perform the test. Basically, it is an alternator test. From the readings, we will know if the alt is the problem. It could be a ground issue, but lets start with this.

https://www.2carpros.com/articles/how-to-check-a-car-alternator

Here are a few links that you may find helpful when testing:

https://www.2carpros.com/articles/how-to-use-a-test-light-circuit-tester

https://www.2carpros.com/articles/how-to-use-a-voltmeter

https://www.2carpros.com/articles/how-to-check-wiring

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Do me a favor, also watch the headlamps to see if the brightness is changing.

Take care and let me know what you find or if you have other questions.

Joe