Apple has decided to replace those units of iPod nano (1st generation) which are facing battery overheating problem due to some manufacturing defect. Affected iPod nanos were sold between September 2005 and December 2006.
Apple says on its website, "This issue has been traced to a single battery supplier that produced batteries with a manufacturing defect. While the possibility of an incident is rare, the likelihood increases as the battery ages."
Apple recommends that you stop using your iPod nano (1st gen) and follow the process to order a replacement unit, free of charge.
Replacement Process
If you are owner of one of the faulty devices, you may order a replacement unit through company's website. Click here to begin.
Your iPod nano serial number will be checked to verify that it is eligible for this program. You will receive a replacement unit approximately 6 weeks after we receive your current iPod nano (1st gen).
But remember, you will not receive the device preloaded with all of your previous contents. So, make sure to back up any data on your current iPod nano before sending it in for a replacement unit. You may use iTunes for baking up your data.