Crankshaft position sensors 'demagnetize' after a while. Some sooner than later. And heat seems to make them less sensitive to signal, causing weird problems.

Just replaced an Audi A4 3.0L quattro Crankshaft position sensor. Its symptoms were as follows:

Cold start/driving were fine. After a 30-min drive, it would make weird sounds, like the engine coughing, 'sighing'.
At a light, the car would stall for no reason or idle horribly, and not want to restart. Just keep on cranking.

CEL was P0321, and P0322. "Engine speed sensor". Replaced it, and now it's all good.