[Lynn Eades]

From a position of no experience of Shermans, save standing on the "Fury" tank, at Bovington, here goes:
Essentially Malcolm, the function is no different from a U.C. drive axle The yellow gears are the spider gears of the diff. When your tank is travelling straight ahead, they are static in the diff carrier. When the Sherman is turned by the application of one brake, the opposite side speeds up by the amount the braked side slows down. (inversely proportional) If you stop one side the rotation speed of the other side doubles. (this does not take into account the extra load and horse power to achieve this)
Anyhow this affects the turn. This diff functions like your average car. Yes, it has extras,(brakes, the hub reduction, size, etc)but the function is the same.

How many times you turn, how tight, What the surface is and probably a whole lot of other things will affect heating of the brakes.
How does a brake work? It converts kinetic energy (movement) into heat. That's it.
Like I said, no Knowledge. I was surprised to find that it never had steering clutches. I guess there's a good reason. I just haven't figured it out yet.