How did you decide they are stopping too quickly and overheating the brakes? The OP did not mention it. It would take a lot of panic braking, repeatedly, to do that. She needs to give more details, but said nothing about autocrossing the car. LOL.
Also, don't forget there is a 400-500lb weight difference between the sedan/coupe and convertible. I have a convertible and have not managed to overheat the brakes. If the car in question is NOT a convertible, they are almost 500 lbs lighter and it would be very hard to overheat the stock brakes in everyday normal use.