Temperature change can build up tensile stresses into thermoplastic materials, if their thermal expansion is hindered. This paper describes how to calculate those stresses. Because thermoplastic materials are time dependent with respect to temperature and strain, a nonlinear viscoelastic material model is necessary for the prediction of thermal stresses. This paper presents a numerical model that is able to predict thermally induced stresses in dependency on the load history. The calibration as well as the numerical procedures are described. The model is evaluated with a semicrystalline high density polyethylene (HDPE). Finally, a simulation of a screwed joint reveals the importance of this modeling for a more effective use of thermoplastics in the future.