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I have had absolutely no issues with mine. It gets slightly warm if I watch movies on Netflix on it, but otherwise no problems. I charge my battery every 3-4 days, though I'm not a heavy user. I can watch an entire 45 minute episode on Netflix and drain maybe 5-8% of battery?
The fact of the matter is that almost any product sold on such a large scale will have defective items, which you then end up reading about on the Internet, but in general I think there are no wide-spread battery or overheating issues.