If you have AppleCare in effect on one of your Macs, the AirPort Extreme is also covered. Get in touch with Apple Support and ask them to replace the AirPort Extreme for you. If you do not have AppleCare in effect on one of your Macs, and the AirPort Extreme is barely over a year old, I would still ask Apple to replace it for you. Nothing to lose
Apple considers the AirPort Extreme a sealed unit, so they do not offer repairs or repair parts for the AirPort Extreme.
If you cannot get the AirPort replaced at no charge, then you might want to open it up using the article that Tesserax provided as a guide. Normally, this would void the warranty, but if you have no coverage, it won't really matter. You might be able to clean out the fan to get it working more efficiently, or find out enough information about the fan to try to locate a replacement online.
Be very careful when taking components out of the AirPort Extreme, as ribbon connectors can break and other connectors may pull loose as well.