Apple has acknowledged for the first time that batteries in some 1st generation iPod nano units sold in 2005 and 2006 can overheat, kill the device, and melt the case. A knowledge base article described the problem, reported on iPod user forums for some time, and indicated support was available, a suggestion that the problem may be covered under AppleCare.
The knowledge base article, "iPod nano (1st generation): Rare cases of battery overheating," describes the battery overheating issue, but calls it "rare" and says it's not associated with a single battery manufacturer: