I think your over estimating your brake temp considerably
Stopping
Mass of bike + rider = 100kg
Speed = 10 m/s (36km/h, about 22.4mph)
kinetic energy = 0.5 m v^2 = 5000J
A basic 180mm steel brake rotor weighs about 150g and the specific heat of steel is about 0.5 J/gK (Joules per gram-degree), so converting 5kJ of kinetic energy into heat in the rotor should increase the rotor temperature by 67 degrees (C), assuming none of the energy is absorbed by the brake pad, caliper body or brake fluid (not realistic, but useful to identify an upper bound for the rotor).
Descents
To maintain constant speed on an even slope, the change in gravitational potential energy must equal the heat energy extracted by braking (plus other sources of friction and drag that we’re ignoring).
Descending a 1 in 10 slope for a 100m distance gives a height change of 9.95m (not 10m, because the distance is along the hypotenuse).
Gravity on earth is about 9.8 m/s^2.
Energy change = m g h = 100 * 9.8 * 9.95 = 9751J
This would increase the rotor temperature by 130 degrees.