I posted the following earlier, but don't expect the person will respond as it's a several year old post. Therefore, I'm pasting it here in case someone can help. Will be at dealership on Friday, but want to have some perspective ahead of time. Things I've read which could be the cuprit are:

1) Heat shield. Looks like they mangled a bit when they installed the O2 sensors recently.
2) Engine mount.
3) Stuck caliper.
4) Transmission issue.

I am actually hoping it's a tranny issue, 'cause that's under warranty (new one put in ~ 1 yr. ago).

Here's the guys post from '05 or '06 and my response:

HIM:

More Engine Noise Stuff

in my almost 2-1/2 year old Cooper, i've begun to become aware of a strange "growling" noise when accelerating hard from 1st to 2nd to 3rd (like when getting onto the freeway from a dead stop) which was not audible in the past. very low pitched, seemingly from directly under the car, and it stops when the revs come up. assuming i'm not imagining this, does anyone have an idea as to what it might be? i suspect something's vibrating, possibly. since i have to take in into the dealer next week for some other stuff, i wanted to mention it but don't want to sound like the technical idiot i am.

ME:

I realize you wrote this quite a while ago, but if you're getting this message, did you ever resolve this sound at the dealership? I am experiencing this very same issue. Thanks.

 

I had the same noise and symptoms once, RPM dependent (yours too?). The noise appeared one day instantly. No lead up or subtlety. It was a rock about 3/4" in diameter wedged between the exhaust and the cross member plate behind the shifter. It was there for a while before I found the rock. Kind of made it sound like I had a meaner exhaust. Still have the rock in my tool box, I should put it back in for autocross...

 

Don't wanna be a doom prophet, but that growling sound under hard acceleration is one the warning signs that the dual mass flywheel is giving up! Hope I'm wrong.

 

Ok, so tell me more about this dual mass flywheel. I'll look up whether it is a component of the tranny. If is, that's covered by my tranny replacement warranty. Would a problem with this component lead to this type of sound under the conditions I described, namely moderate to significant acceleration?

 

Ok, read briefly about it and it seems this is a component of a manual transmission vehicle. Mine is an automatic CVT, so I don't think this is the culprit...

 

RPM-dependent? Well, if you mean within a certain RPM range, then maybe... Not sure. All I know is that when I accelerate hard enough (typically notice it in the ~1.5-3k range, but it could certainly happen at higher RPMs), I hear that aggravating growling noise. The car will be in the shop Friday. Will see what they have to say about it... Came on suddenly. I know you've heard this question before, but is that you in your little graphic that accompanies your posts?

 

The dual mass flywheel (DMF) controversy is a real can of worms. The DMF is not a part of the tranny. It can fail at any mileage and it takes the whole clutch assembly with it. Even under warranty most dealers won't cover it claiming driver abuse. This is nothing new. Valeo issued a service bulletin on the problem in Jan. '07. That bulletin also detailed how to tell if it was driver abuse or DMF failure. All manufacturers are aware of the problem with Ford first discovering it in 1992 on their big block pick-ups!

 

This is a manual transmission only problem, though, right? I have an automatic CVT, so I guess this is not an issue that would be causing my problem... Please confirm. Btw, there is no real drivability issue for me, except that if I don't want to hear the sound, I have to increase speed more slowly so as not to have to more "aggressively" hit the gas... Kind of the old person syndrome, if you know what I mean.

 

Yup, the DMF problem is only on manual transmission MINIs.

 

Oh, a CVT... It might be something internal to that. The dealer should check for any TSBs related to the CVT.