You may need to adjust the screen off settings under display. If you don't want to continuously adjust the settings when you are driving/not driving, then consider using an app called "Tasker". It allows you to set a lot of actions based on the conditions created. For example, you can likely set the screen to stay on while connected to a charger during the day.
Let us know how things go.
I was already pointed to an app called Llama, which I'll try first. If that fizzles, I'll take a shot at Tasker.
It's actually more than just the car. I use Roaming Squirrel's superb scientific calculator at work, where I also have a charger. So, the bottom line is I don't want to the screen to auto-dim or auto-shut off while on the charger. I will (when I find time) experiment with Llama (and maybe Tasker) and report back what I find to this thread.
UPDATE: Llama appears to work fine for this. It was easy (intuitive) to set up this one usage -- there's lots of other things Llama can do, but right now keeping the phone on while on the charger was my only concern.
The Smart Action "Adjust my Display Sleep" action appears to conflict with Llama, so you'll have to remove that Smart Action if you're currently using it, but that appears to be the only issue.
According to GSam, Llama when used in this one configuration draws no battery power.