The discussions on this forum about brakes overheating causes me to wonder: Which system is fundamentally better at dissipating heat: rim brakes or disc?

A thought experiment: A tandem team descending a steep mountain road with tight switchbacks. The switchbacks are tight enough to cause the team to repeatedly have to slow way down to make the turn. This situation is severe enough to cause at least one of the brake systems to experience some failure.

They have two identical bikes - except that one has the "best" caliper rim brakes and the other has the "best" disc brakes. They descend this road on each bike under exactly the same
conditions.

Which system is likely to fail?

Brakes basically turn kinetic energy into heat and dissipate the heat to the air. A disc is steel and can get much hotter before it fails. Heat transfer occurs faster at a higher temperature differential. A rim is aluminum, much larger and likely moving at a higher rate of speed through the air. If the rim gets too hot, the tire is likely to blow off.

Under the most taxing conditions, which works better?