While driving my 2012 A4 Quattro yesterday, a very loud alarm beeping came through my speakers. I turned the radio off and the beeping continued but none of my alerts displayed or lit up on the display panel. The noise continued for about 2 minutes then stopped. I noticed no change in handling of the car during this time. What was this about?!

If no warning light from your display, then you have a beep for temperature change. For example on my car when the outside temperature drops below 4 degrees celsius I heard
a sound like a beep. But it does not take more than a few seconds!