The aim of this thesis is to develop and test a reliable one-dimensional physical model of heat diffusion within the brake system of a car. The ITT company has been able to develop a brake pad, termed Smart Pad, that is endowed with sensors installed on the backplate, in particular a temperature sensor. The long-term goal of the research project developed with the ITT company is to use the data from this sensor to prevent the brake from overheating by estimating the disk temperature in real time. Since the backplate and the disk are the two opposite sides of the friction material it is necessary to model the heat propagation inside the pad.