I had no problems at all with the upgrade to 8, didn't do 8.0.1 but on Sunday I applied 8.0.2 to my devices (iPhone 5S, iPad Mini, iPod Touch 5th gen). No problems at all until this morning, and only with the iPhone.
Using my 4G I updated four apps and downloaded a book from the ibook store. Went to ibooks to read the book, read the first chapter and ibooks crashed. Opened the book again, back to the start and found that my setting to not show books in the cloud had reverted to showing them, went to chapter 2 and started reading, crash. Re-booted (held down off and on switches) and tried again. Got a bit further before the app crashed. This time the phone was very hot, something I have never experienced before other than the minor heat when re-charging the phone. Shut the phone down completely and left for 20 mins to cool down. Turned on again and returned to ibooks, same book, read a bit, crashed and phone becoming very hot within maybe two minutes.
Phone off, cooled it again, turned on and tried several apps none of which heated the phone. Opened ibooks again, deleted the book I had downloaded just in case that was the reason it was heating. Turned phone off again without doing anything else, back to ibooks, read another book and although it took a little longer, the device heated up. Battery meanwhile had drained considerably since I first turned the phone on, visibly dropping by 1% for each page I read of the book.
Device currently charging via battery doctor.
No problems at all on my iPod or iPad - I considered replicating the above on one of these but decided against it as I don't need two devices overheating.