Solid-state fermentation (SSF) has potential advantages for the production of certain biotechnological products, due to its large volumetric productivity and low operating costs. However, there are major challenges in obtaining adequate heat and mass transfer when this fermentation method is used at large scales. Mathematical models and computer simulations are useful tools for designing strategies to overcome these challenges, given the cost of large-scale fermentation experiments. In the current work, we used the commercial CFD software ANSYS FLUENT® 16.0 to develop a mathematical model for heat and mass transfer in a pilot-scale packed-bed bioreactor. The model takes into account the dynamics of airflow in the porous substrate bed and the lack of thermal and moisture equilibrium between the solid and gas phases. The permeability parameters were obtained from pressure drop measurements made in the pilot-scale bioreactor during a fermentation in which Aspergillus niger was grown on a mixture of wheat bran and sugar cane bagasse. The CFD simulations were able to represent the temperature and moisture profiles observed experimentally during the initial heating of the substrate bed by the process air. A parametric analysis was also performed, in order to understand better the physical dynamics of the system. Our work provides the basis for the development of a robust and reliable model for testing operating conditions and control strategies for large-scale cultivation in SSF bioreactors.