I just started troubleshooting a similar sounding problem on my 2001 3.0i. I don't want to confuse things in this thread, so first a question - how relevant are things on the OP's 2006 3.0d to my 2001 3.0i?

My symptoms are almost exactly the same as the OP. Spent some time yesterday troubleshooting things for the first time.

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2001 X5 3.0i, 203k miles, AT, owned since 2014