I do wonder if the dock would help prevent this, if the dock were white.
I doubt it. I drove from Quantico, VA to Frederick, MD and back today (1.5hours each way) and it didn't have a problem for the first 45 minutes then it started getting hot. I'd put my hand on the dash, after taking it down, and the dash was boiling. I was out of the car for a couple hours but around 30ish minutes in the car again it shut down.
I drive from Baltimore to Quantico, about an hour drive, a few times a week and haven't seen this until the weather started warming up. I use it when I drive for traffic all the time too.
I just installed a battery temp monitor and on my next trip I'm going to watch it to see what happens. I've left the gps unit on in my house while charging and it's been fine for the last 2 hours. So it has to be the damn sun.