One thing you could look into is a new diff cover. I replaced my stocker with the finned cover from the Boss 302/GT500. Does it help? I'm not sure but I would guess as its on those cars and many heavy duty trucks (high temps for towing).
A friend of mine with an E46 M3 (a good bit less powerful than your M3) has a VAC diff cover.
Something like this
https://store.vacmotorsports.com/vac-finned-differential-cover-bmw-e82e87e90e92e93-p2493.aspx
A friend of mine with an E46 M3 (a good bit less powerful than your M3) has a VAC diff cover.
Something like this
https://store.vacmotorsports.com/vac-finned-differential-cover-bmw-e82e87e90e92e93-p2493.aspx