This paper reports a numerical approach for modelling the thermal behavior and heat accumulation/liberation of sustainable cementitious composites made with Recycled Brick Aggregates (RBAs) employed as carriers for Phase-Change Materials (PCMs). In the framework of the further development of the fixed grid modelling method, classically employed for solving the well-known Stefan problem, an enthalpy-based approach and an apparent calorific capacity method have been proposed and validated. More specifically, the results of an experimental program, following an advanced incorporation and immobilization technique, developed at the Institut für Werkstoffe im Bauwesen for investigating the thermal responses of various combinations of PCM-RBAs, have been considered as the benchmark to calibrate/validate the numerical results. Promising numerical results have been obtained, and temperature simulations showed good agreement with the experimental data of the analyzed mixtures.