There's no objective answer because there are too many factors to consider.
I ride three tandems: a Ventana MTB with two pot Magura hydraulics, a Santana with V-brakes, and a Paketa with the Shimano road hydraulics. Do I miss the disc brakes on the Santana when I ride it? Absolutely
... not. In fact I'd say I'm more carefree with the older technology. I can carry extra cables to backup if there's a failure. They are quiet (no "schwing-schwing-schwing" after heavy braking), I don't have to worry about bending rotors if I need to get the wheels off and on in a hurry or on the side of the road. The pads last almost at least 2-3X longer, are cheaper and available anywhere. They're cleaner - they don't leave grimy brake dust all over my fork and chainstay. With 32mm tires inflated to 85-88 PSI there is plenty of thermal expansion buffering in the air chamber to not worry about blow outs.
The Shimano hydraulics are fiddly and can be a pain to keep up and maintain (Bleeding on initial setup. You have to pull the pads to check wear. Oh, did I mention the dust?).
The Maguras have been worry free, but they're ~2004 vintage (before weight savings were a factor leading to compromised design) and they don't get a fraction of use as the Shimanos.
Yes, the Shimanos work and feel great and require less pressure at the lever. I've ridden them in the wet including two downpours. But, I didn't ride the bike any faster or less cautiously than I would have with rim brakes. So I honestly don't think they gave me any advantage whatsoever over rim brakes. Mud clearance, grit and other extremes of off road riding are a better argument than wet performance.
They're just two slightly different modes for doing the exact same thing. One is only "better" than the other insofar as it meets your real-world needs, desires and expectations of performance, reliability, aesthetics, maintenance, cost, weight, aerodynamics and on and on.
Any "objective" heat data would have to come out of a laboratory environment, (i.e., not applicable to real-world use, since so few of us ride our bikes in a laboratory). Some acceptable level or benchmark of heat capacity for all components involved would have to be established which of course is much easier to do with the disc brake systems. You can be sure that Shimano, SRAM, Magura, Et al. have done that with their products. But what is the baseline for rim brakes? Again, just lab coat data collection - and to what end when you finally compare the two?