If you have a first-generation iPod nano (the one that looks like a slimmed-down version of the iPod video and comes in only black and white), you may be able to get a replacement or a fix from Apple, depending on what kind of symptoms your device is exhibiting.
Specifically, Apple acknowledged via a knowledge base article that the early nanos have a tendency to display battery overheating problems, an issue that it seems like every one of its production mobile devices is accused of at one time or another. The article posted by Apple does admit to the problem in the 1G nanos, but it sure goes out of its way to downplay its significance, as is evident from the following passage:
Apple has determined that in very rare cases, batteries in the iPod nano (1st generation) sold between September 2005 and December 2006, may overheat and prevent the iPod nano from working and deform it.
Apple has received very few reports of such incidents (less than 0.001 percent) and the issue has been traced to a single battery supplier. There have been no reports of serious injuries or property damage. Additionally, there have been no reports of such incidents with any other iPod nano model.
Discoloration, overheating, and case deformity near the battery are all symptoms of the problem, so it should be fairly easy to tell if your model is affected. Remember, though, that there’s overheating and then there’s just plain heating, which is something all Apple devices do even when in fine working order.
Interestingly, if you do a quick and dirty Google search for nano overheating woes, you find no shortage of pages like this that seem to indicate that Apple users were well aware of the tendency a full four years before Apple decided to acknowledge them. If you bought your device in 2006 and you paid extra for extended AppleCare service, you may still be covered, but it’s unclear whether devices not under warranty will be eligible for replacement.
If I was the suspicious type, I’d think it highly unusual that Apple would wait this long to acknowledge a problem that seems to be fairly well-documented in the past. Even if it is providing replacements for those without AppleCare, which seems to me unlikely without an official announcement of an extension of eligibility, the timing means that many nano owners will already have ponied up for a newer model, or an iPhone.
If you have an affected model iPod nano, do us a favor and contact AppleCare and let us know how Apple responds.