Brake fade is all about the pads and other parts.

Rotor diameter and and thickness, as well as internal vane design and air gap, affect how much heat they can absorb and shed. All else being equal, a larger mass rotor will run cooler as will one with more internal air flow.

However, the main issue here is that brake fade is caused by either exceeding the maximum operating temperature of the pads or exceeding the boiling point of the brake fluid. Fluid fade is characterized by a sinking brake pedal. And pad fade is characterized by a firm pedal, but dramatic loss of friction. BOTH of those issues can be addressed by changing to a pure race pad, such as Hawk HT-10 which can work up to 1600 degrees, and replacing your brake fluid with Motul 600 or Castrol SRF. Motul 600 has a dry boiling point of 593 degrees F which is more than 50 degrees higher than ATE Super Blue Racing.

If you're looking for a wider range of conditions under which street pads will work without fading, then yes, bigger mass rotors are the answer. But if you are tracking the car, even with bigger rotors, you really should be swapping pads back and forth between street and track. Using the same pads all the time is like someone in New Hampshire running at NHIS with all season tires because they need something that will work on the street in case it snows! In both cases, you are leaving performance on the table by compromising.

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Rotor diameter and thickness (better cooling and more surface area) is more important than bigger "pots" on the same diameter rotor.

As a matter of fact, a larger caliper would cause the brakes to fade faster due to increased "clamping" power.

That's not true. At the track, the driver should always threshold brake regardless of the caliper piston size. Since clamping force is a function or piston area times system pressure, the driver merely has to press more lightly on the brake pedal to achieve the same clamping force required to threshold brake. Anything more than this will lock up the wheels.

Of course, if the clamping force is changed in the front only, then the balance of brake torques will be thrown off and the stopping distances will increase because the rear brakes aren't doing their fair share of work. In that case, yes, the front rotor temperatures will be higher because the system is not balanced.