Thanks Peter, will be interesting to find out.
8 miles, didn't go under the car, too wet, but using an Infra Red thermometer there was no real difference between the diff and any where elae in the area, about 4c.
FWIW the Merc dif has to deal with 238 bh and 399 ft lbs torque. Yes, it is a diesel. But a bit more than the M3W. I don't accept that a properly designed, constructed and assembled bevel box should generate any significant heat.
A noisy box is wasting energy, noise is energy. No surprise that noisy boxes also get hot. A crude simple bevel box needs lubricating with an EP oil, not grease. The oil helps to take heat away from the teeth meshing. But a modern box shouldn't need to remove much heat and a thicker oil would be better.
I'd love to see inside one of these boxes, I'd also love to see the specifications for set up, getting the teeth to mesh correctly requires precise manufacture and careful assembly.