Environmental challenges in the building sector have made raw earth a significant ecological alternative. The development of sustainable materials and a clear understanding of their behaviour are essential for sustainable construction. This work aims to respond to this societal issue. This investigation uses a HAM-BES cosimulation methodology that integrates dynamic thermal simulation code (TRNSYS) with a hygrothermal transfer model developed by Luikov and solved by Comsol Multiphysics. The study aims to investigate the energy needs of different building envelopes in several climates where there is raw-earth architecture. A comparison between a cob monolayer envelope and a polystyrene insulated polystyrene insulated brick multilayer envelope has been carried out. This study shows that the raw earth monolayer wall has a higher energy need for oceanic and tropical climate with, respectively, 14 and 19%. A decrease in demand has been found for the desert climate. Moreover, it was shown that the coupling of heat and mass transfers results in a notable reduction in energy demand that can reach 11.5% annually and up to 23% quarterly for tropical climate. These findings highlight the efficiency of raw earth materials and stress the importance of thoroughly understanding and incorporating heat and mass transfer dynamics in the evaluation of sustainability for biobased and earth-based construction materials.