Finite Element Methods offer an enormous industrial potential for the cheap design of parts. However, the opportunities of simulating entire (hybrid-)production processes mostly remain untapped. This is due to the fact that contact between different surfaces and materials is oftentimes prone to systematical errors. The bachelor thesis at hand addresses this problem and presents different approaches for the realistic contact simulation between different surfaces. In this context, different constraint enforcement methods such as the Augmented Lagrange Method alongside different pressure-overclosure relationships are presented. Another focal point in this bachelor thesis is the realistic simulation of heat distribution. Example of use is a hybrid forming process in which a steel barrel is inductively heated and forged - thereby creating contact between the workpiece and the forging die.