Confirmed.
Layered a folded thick beach towel in the open space and over the silver module (is that for stereo, I dont have idrive). Observations:
1. Cold start did indeed have a tad less rumble inside the cabin with windows up.
2. Warm idle and stationary throttle blipped also invoked a tad less rumble.
3. 2k to 3k rpm in 5th gear with light throttle application - noticeably less drone as well
4. After 7 miles in mid 70s temps, I removed the towel which was noticeably warm.