I've read from F1 articles that heated air travels faster. From the picture of the M3's rear undercarriage, it does seem there's a lot of heat created just before the rear diffuser from both the exhaust silencer and the M differential's heatsink. I would think the heated air is accelerated through the diffuser to create downforce and cool the M differential at the same time.
But the M3's underbody does look pretty messy at the rear with many exposed mechanical components. Wish they would clean up the airflow of the car by testing it in their F1 windtunnel at Hinwil. It's no coincidence cars like F430, R8 etc have their undercarriage almost totally covered.