This has happened to me several times: I’ll pick up my iPad to discover it has shut itself off, or at least has a black screen and won’t respond. Not because of overheating, and not because there’s no battery left. And it just won’t turn back on. At least at first. And sometimes not for quite a while. It’s pretty scary.
A little research shows that others are having this problem, sometimes even with an iPhone. The cause is unknown, but the best theory is that it’s some type of kernel panic. The quickest solution? Hold down both the home and sleep buttons for about 10 seconds to do a forced shutdown. The iPad should start again with no problems.