Temperature fields generated in machining processes affect, among other internal material loads, the material modifications in the workpiece surface layer and therefore influence the functional performance of the final component. In particular this might become critical for multipass machining where the amount of heat in the workpiece is accumulated with every path and layer being cut. In the present work a finite element modelling approach for the milling of a complete steel plate is proposed that minimizes computation time while providing a reasonable accuracy of predicted temperature fields. The milling process is modelled as a moving heat source taking into account material removal. Computation time can be reduced up to 98% by systematically increasing the width of the material removal and the heat source width. The effects of the model reduction regarding the temperature fields are investigated in comparison to a reference simulation and furthermore to experiments.