The research project at hand deals with problems, which are determined by the interaction of mechanical and thermal quantities during the contact of two or more bodies. The effects caused by friction, heat transfer and heat generation as well as thermomechanical interactions in the material are considered. Such models are used in the simulation of many processes in production engineering. They are getting more and more important because of environmental and economical reasons. The numerical simulation of such kind of problems lead to a huge computational effort. Hence the application of modern discretization techniques like adaptive finite element methods is indispensable. The aim of the research project at hand is a basic step to adaptive space-time finite element methods on the basis of goal oriented a posteriori error estimators. It consists in the development and implementation of a finite element method in space and time on locally refined meshed. To this end, we construct suitable ansatz space and deduce the resulting time stepping schemes. Finally, efficient solution algorithms in every time step have to be realized.