Hello slugg_04,
We understand you're experiencing an issue with the your iPhone lagging when connected to CarPlay.
Get started with the steps here: If you need help with CarPlay.
You may also want to check to see if there is an update for the stereo that needs to be installed. You can find how to update it in your vehicle manual.
You also mentioned that your iPhone appears to be overheating. There's a great article that goes over the temperature management of the iPhone here: If your iPhone or iPad gets too hot or too cold - Apple Support
If you're seeing an alert that your iPhone needs to cool down, it mentions "An iPhone showing this message might still be able to make emergency calls. To resume use of your device as quickly as possible, turn it off, move it to a cooler environment (away from direct sunlight), and allow it to cool down."
We'd recommend removing any cases or screen protectors that could be affecting the temperature of your device as well.
Let us know if you have any questions.
Thank you for using Apple Support Communities.
Take care!