I use Android auto in my Chevy. It progjects the screen to the car and turns the note-3 screen black. During a 30 minute drive the note-3 gets noticable hot.
Welcome to the forums. Even though the screen is off on the phone it's still doing all the work to project that data to much larger device. That takes power, which produces heat.
If you need additional help or have more questions or details to share, please join the site so you can reply in this thread. See this link for instructions on how to join Android Central.