A heat transfer model of a semi-industrial induction furnace has been build, using a 3D finite element model in order to analyze the entire process cycle, based on the heating, melting, solidification and cooling phases of a multi-crystalline square ingot. In the modeling of the entire process, heat transfer phenomena such as radiation and conduction in the furnace have been taken into account. A PID (Proportional Integral Differential) control algorithm has been implemented into the model for adjusting the power input in the heaters, so that the heater temperature is kept at prescribed time-varying values. The furnace model and the PID control algorithm are validated by temperature measurements from a crystallization experiment. Subsequently the validated model was used to investigate the melt flow field and its impact on the solid–liquid interface shape.