This is a cutaway view of both the tank and the cooler. The studs are inside the cooler. They accomplish two things. First, as you rightly suspect they increase the area in contact with transmission fluid. The second reason they are there is to disrupt laminar flow, as turbulence improves cooling by causing more fluid to impinge on the studs.

If you slice open a radiator tube on a modern core, you would find that the tube is corrugated for the same reasons. Modern fins are also corrugated, and some are slit, because the same considerations apply to the air side.