aluminum vs. steel in brake disc
The temperature limit of an aluminum rotor is about 350° F. The limit of a cast iron rotor is about 1200° F. If steel is used, the temperature limit will be around 900° F. The heat capacity of the rotor will be a function of specific heat and weight which you don't know yet beacuse that's what you're solving for. Steel and cast iron have a specific heat of about 500 J/kg-K. Aluminum is higher in heat capacity than steel at 890 J/kg-K but since the Al rotor probably weighs less the heat capacity may be about the same. Emmisivity is very low at about .1 for aluminum but is around .4 for steel. Convection and emmisivity control the cooling rate unless your design allows for conduction through the hub or wheel. Anodizing and dyeing the inside of the aluminum rotor black may improve the cooling. These may raise the emmisivity to around .25.
At the end of your calculation, I believe cast iron brake rotor will be the better design. Only ceramic and titanium have been used successfully to reduce unsprung weight for long-term applications.