The biggest issue with mine off-road was the hinges on the screen. I have a pop-out fold-up dash single DIN unit and on really bumpy roads the screen would start to fall over. No big deal, just push it back up, but frustrating when trying to use the GPS to navigate. I haven't had it happen recently, but can't remember if I got around to tightening up the hinges, or if my roads recently just haven't hit the right frequency.
As to heat, I have a Mac mini with an internal heat sensor. When it gets to hot it automatically shuts down to protect itself. I've had this happen once, this winter. The mini is under the driver's seat and I had the rear heater on full and it is angled to blast right underneath there. A minor future mod is to make a block off plate so the heat is never directly on the mini again.
I haven't tracked internal temperatures (hmm, perhaps I should) but I've never had it shut down due to heat any other time.
My screen on the other hand can be finicky. If I start up on a cold day or very hot day it will display a constant color, but the touchscreen will still work. Usually if I put the computer and screen to sleep and wake them up again it will be fine, sometimes I have to resort to restarting the mini, but that has never failed to work. No one else has reported problems with my particular make of screen though.
Cheers,
JFS III