idles rough when cold

The idea that it only runs rough when cold makes me question if there is an issue with the coolant temperature sensor. The computer uses info from the sensor to adjust air/fuel mixture. If it's not accurate, it can cause this. Now, the easiest way to check is with a live data scanner. What you need to do is simply compare the temperature reading to the actual outside temperatures.

Now the idea that you only get the misfire code what cold could indicate a compression issue or even a simple vacuum leak. When the engine warms up, steel expands which could allow compression to change. A vacuum leak may be more noticeable when cold as well.

Before we jump too far into guessing, when was the engine last tuned up? Have you done any checking for vacuum leaks?

Here are a few links for you to look through. See if they help and also, let me know what has been done (if anything) and if you have a live data scanner. If you do, let me know what the fuel trims are and what the coolant temp sensor is indicating.

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https://www.2carpros.com/articles/engine-misfires-or-runs-rough

https://www.2carpros.com/articles/how-to-use-an-engine-vacuum-gauge

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I will watch for your reply.

Joe