take your belt off and run the engine after it’s warmed up of course. Definitely sounds like a bearing situation and I have worked on a car where the tensioner wore out and was angled a little bit I was actually able to repair it by cutting a counter angle in the mount.

That’s sad day when it warms up factor hints at a problem with the fan clutch. You can again wait for it to warm up pop off the fan And see if the sound goes away.

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2011 E70 • N55 (me)
2012 E70 • N63 (wife)