The advantages resulting from the use of numerical modelling tools to support the design of processing equipment are almost consensual. The design of calibration systems in profile extrusion is not an exception. However, the complex geometries and heat exchange phenomena involved in this process require the use of numerical solvers able to model the heat exchange in more than one domain (calibrator and polymer), the compatibilization of the heat transfer at the profile-calibrator interface and the ability to deal with complex geometries. The combination of all these features is usually hard to find in commercial software. Moreover, the dimension of the meshes required to obtain accurate results, results in prohibitive computational times for industrial applications. This work reports the development of a new multi-domain parallelized solver in OpenFOAM® framework, that comprise all the features required to model the heat exchange in the calibration/cooling stage of thermoplastics profile extrusion. For this purpose, and having in mind the possibility of performing optimization and parametrization studies, automatic geometry and mesh generators were also developed and the modelling routines were coupled with an optimization software, Dakota (https://dakota.sandia.gov/). To assess the implemented solver the results predicted by the code are compared with analytical solutions, by using the Method of Manufactured Solutions, and with other results available in the scientific literature. The usefulness of the new solver is illustrated in a few case studies, used to evaluate the effect of the major process parameters and system geometry on the profile cooling performance, some of them involving specific optimization studies. The results obtained emphasize the practical helpfulness of the developed solver, which is able to deal with complex geometries and large dimension problems, providing useful and additional insights to the process.