Less heat since they are bigger... more force because they have more leverage.
No, not really. But yes, maybe you're right.
Brakes work by converting kinetic energy (energy of motion) into heat. The Law of Conservation states that energy is never created nor destroyed. Kinetic energy is transformed into heat through frictional forces. The faster you can convert it, and the more heat you can hold, the better the braking power will be. That's why carbon brakes are so good, btw.
So the bigger rotors produce more force by creating more heat. That's just as simple as it gets. Primarily this happens because for a given speed, the outer circumference of the larger diameter will be traveling faster than a smaller diameter rotor. The advantage of the bigger rotors though is it is able to shed that heat quicker as well.
So if you're trying to state that, in this case, the bigger rotors will be able to shed more of the heat quicker and the rotor carriers/hub will be cooler, you may be correct in that statement. But saying they will run cooler overall isn't a true statement.
For the purposes of this thread, the wheel hubs were beefed up to accommodate the bigger brakes and more braking forces and that's why the part numbers are different.