Abused Power Outlet
According to Audi, with regard to 2009 Cabriolet A4 models, if the cigarette lighter/12-volt accessory outlet will not heat, the retaining tabs in the lighter socket are pushed out too far of the socket to hold the lighter element in place for the heating process.
Generally, this is caused by using the lighter socket as a power outlet for accessories such as cell phone chargers, radar detectors, etc.
Remove the cigarette lighter fuse and remove the heater element. Using a flat blade screwdriver, bend the retaining tabs inward. Reinstall and test.