I might have a similar problem (although the radio is not affected, but mine is rewired and aftermarket). My symptoms: when it is really hot outside (over 95) and the car has been sitting in the sun, the ac will turn off and back on when I slow down or brake hard. I can see the ac display flicker, and it resets itself to the temperature and fan speed I had when I first turn on the car (I guess there is some type of memory).
Long and short, what solves the problems is to disconnect and reconnect the instrument cluster. There seems to be a bad contact that misbehaves when the inside of the car is really hot. I never figured out which contact or which wire, or if the cluster needs to be replaced altogether. But, apparently, there is a ground that must be misbehaving (or at least that was my best diagnosis).

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2008 S550
2010 GLK350
1997 E420 (retired)
2005 CLK500 (retired)