Things that usually make an iPhone feel warm/hot: battery charging (charge faster, heats up more), CPU is working hard (check your apps and what’s running in the background, and sometimes after an iOS update has had problems with battery drain because there is some app or process), and passive cooling decreases when it gets hot (phone case, believe it or not, pocket lint).
If I’m using my navigation and podcast player under carplay, and my phone’s screen is 100% and not put to sleep, and the case is on and charging, it might be warmer than the sleep screen doing GPS or CarPlay, but not particularly warm.
I don’t think CCU is specifically making your phone work any harder than Ford Sync (which I had twice before, albeit with older phones). You can buy a USB-A voltage tester to see how much power it’s putting out (likely 2.1a or less). You can also connect your phone to a Mac Console or XCode running to check the crash logs, which will tell you that everything is running. If you want to compare the two cars against each other, I would try to check the conditions (doing all the same things in the same conditions) and see where and how it gets hot.
If your phone is under warranty or AppleCare, I’d also start by opening a support case with Apple before contacting SOA: for a specific CarPlay issue they’ll send you back to Apple to troubleshoot.
