How hot do brakes get? Very. Very hot.
Check out this test of the rear disk brakes of a Honda S2000. Using a thermal camera, Engineering Explained is trying to observe the amount of heat generated by those rear brakes at different spots on the rotor. By revving the engine to 3000rpm and pulling back the hand brake at the same time gets to temperatures close to 300F. While he mentions that brake rotors can reach temperatures of 1,000 F on a track day, this particular test was done with the emergency brake, which doesn't even replicate the full stress of everyday braking. Clearly, brakes get hot, fast. But we already knew that, right?
Related: A thermal camera shows how much abuse a tire receives during a burn out