© 2020, Springer Science+Business Media, LLC, part of Springer Nature. The experimental acquisition of data for monitoring cereal grain storage in silos for long periods is not practical in most cases; in such situations, mathematical modeling is an excellent alternative to predict temperature and mass transfer behavior. The model was developed in two dimensions using the equations of heat, mass, and momentum transport. The governing equations were solved using discretization of the spatial coordinates by orthogonal collocation with Jacobi polynomials and the resulting algebraic system was solved by employing nonlinear relaxation method that uses less computational resources. For the ambient boundary conditions, it was used as a more accurate equation to represent the diurnal–nocturnal temperature dynamic. This study analyzes the effects of moisture migration and temperature interactions between the interstitial air and the sorghum cereal grain bed defined as a porous medium in a cylindrical cavity, including the variations affected by meteorological conditions over 1 year. The mass–thermal gradients were predicted, and the effects of environmental temperature were analyzed for flow patterns, isotherms and moisture distribution changes, indicating how the environmental fluctuations influence the heat and moisture of the ambient spots in the grain storage. The maximum temperature inside the silo was 42 °C, considering the respiration heat of the grain, and the maximum temperature of the grain without the climatic boundary conditions was reported to be approximately 35 °C in previous studies. The proposed model can be easily extrapolated to be used for other cereal grains or to incorporate additional effects such as solar radiation, shadow sunlight path, wind velocity, equations to predict more precise ambient temperatures, etc. as boundary conditions.