Answering your question in general, (while not pertaining to bicycles) drum brakes dissipate and store large amounts of brake energy instantly as well as for a limited amount of time.
Slam on the brakes in a fully loaded high speed 18 wheeler, for example, and up to 3000 hp can be instantaneously absorbed for a very short period of time by the brake drums, making them literally glow red hot.
Just look at the brake drums of a vehicle used in serious repetitive downhill transport and ask yourself how all that heat checking happened if the metal did not reach red hot temperatures. As well with the bluing, etc.
Assuming that the rig reaches the emergency stop or the bottom of a hill before the brake drums expand away from the shoes (called brake fade), then as the rig continues along its journey, the brake drums cool off by transferring that heat to the atmosphere (and the wheels and tires, sometimes causing blow outs) until the temperatures equalize to the ambient.
Once the brake drums are cool again, the process can repeat itself over and over.
Disc brakes, on the other hand, because their advantage is that they are lighter and have less mass, will not fade. They will stay in there and will destroy themselves while saving the rig. They will absorb the same large amounts of energy as well.
So while the drum brakes on a crashed vehicle that runs away and crashes due to brake fade will eventually cool off and be functional again, not that the wrecked vehicle needs brakes any more, the brakes on a disc braked vehicle may have to be relined at the bottom of the hill, but they will go and go and go until they destroy themselves before they will fade and lose the rig.
So, on a downhill application that requires lots of brake applications, give me drum brakes any time. In an over the road application in regular traffic, give me disc brakes. (I can add heavy retarders that keep me from using the brakes excessively, saving them cool for panic stops.) I just prefer their storage capacity over discs.
While this is the theory, I doubt that it pertains to a bicycle. But you asked. As far as formulae, SAE has done a lot of research on drum as well as disc brakes. Try
rmw