I have the same problem. Although mine does not seem to care if the motor is cold or at operating temp. And it is intermittent. My guess is a collapsing lifter. It only takes one or two seconds for the noise to go away and then it is quiet. Car is an 05 330I with 68K. Well maintained previously and currently.
I am fairly new to the E46 and motor issues so I am not sure what else could cause this. Has anyone had an issue with lifters on these cars?