The description of the specific volume under practical conditions during the processing of plastics still poses a challenge. For the processing of thermoplastic materials, the cooling process is particularly of high relevance. Since integral values for the specific volume are determined with conventional measurements, the local temperatures and cooling rates must already be taken into account during the evaluation of the measurements. The non-isothermal effects are difficult to determine with current analytical devices and yet lack a mathematical model that describes them sufficiently. In this work, the authors present an approach, which considers local temperatures and cooling rates. This is a basic requirement for the optimization of cooling rate dependent material models. This approach is implemented by means of numerical methods using the example of an amorphous thermoplastic material. The results, which are based on a cooling rate-independent model, are promising and set the base for further work with cooling rate-dependent constitutive models.