A magnetic and temperature field-coupled mathematical model is proposed to calculate the induction heating process of a discard substitution block for billet hot extrusion process. The mathematical model is validated by comparing simulation results with temperature measurements recorded during physical modeling. Based on systematical analysis of calculation results,a quantitative sawtooth induction power curve was proposed to realize the aim of achieving the best distributed temperature field in the block within the shortest induction time. A magnetic and temperature field-coupled mathematical model is proposed to calculate the induction heating process of a discard substitution block for billet hot extrusion process. The mathematical model is validated by comparing simulation results with temperature measurements recorded on physical modeling. Based on systematical analysis of calculation results, a quantitative sawtooth induction power curve was proposed to realize the aim of achieving the best distributed temperature field in the block within the shortest induction time.