That's a couple curious iPad issues. I use my old iPad 2 and I run all day with a Dual 150 NOT plugged in at all to exercise the battery and I still have plenty of battery left. Its kept on the mount without the need for a case and I've never had the need to run the screen at full brightness because it's not mounted close to the windshield. I've never had an Apple device overheat or otherwise fail. Hell, I have a first gen iPod mini that still works somewhere around here. I'm not trying to praise Apple products but I've had/still have a bunch of them and they've been bulletproof.
You obviously don't live anywhere hot haha. Apple devise overheating is a common thing out here. 20 minutes in front of the AC and you're normally good to go. I've had it happen to my phone just sitting on the trans tunnel on my E30