It's not really free. After getting my serial number validated, Apple sent me an email with the following fine print:
"Apple may charge you a diagnostic fee, including shipping charges, of no more than one hundred ($100) dollars US, plus applicable tax, if Apple inspects your product and determines based on the inspection that the product does not require service. If Apple determines, while inspecting your product, that service is needed due to the failure of parts that are neither supplied by Apple nor Apple-branded, Apple may return the product to you without servicing it, and may charge you the diagnostic fee plus applicable sales tax. "
Thus if your ipod nano does not exhibit signs of overheating, Apple will charge you a service fee of around $100. Not worth the gamble.