Overheating Airport 3TB, fan noise

I've had this unit for a 12 month period and it has been faultless. Recently though, I noticed an intermittent "buzzing", which would cycle on and off, sometimes for days. Today however, I have been getting "This device may be overheating" warnings and the noise is MUCH, MUCH worse.

I can probably get the unit swapped by the retailer, but I want ot preserve the 1.25 TB of data on the HDD as it has all my Time Machine backups on it.

How do you pull the data off the Airport so that it can be restored to the replacement unit?