By punch trajectory planning for a multi-axis forming press, it is possible to affect the local material properties in the workpiece. A multi-axis forming process can influence the material flow and thus the material properties via the punch path. During multi-axis forming processes, the velocity on a defined punch path affects the heat transfer between the punch and the forming material. An example for such forming materials is glass mat thermoplastics (GMT). Multi-axis forming can form these materials in a molten state. The materials cool down during forming due to contact-induced heat transfer between material and punch. The contact zone varies during the process and depends on the punch path. The punch velocity, however, influences the duration of the contact. In order to plan the punch velocity for required part properties, this paper presents an analytical model. The model bases on the geometrical description of the contact zone and gives different velocity profiles, which are tested in experiments. Finally, the paper discusses the analytical model, the velocity profiles and the requirements for the press.