During the storage of granular materials such as cereals, sugar, salts, polymers, etc, moisture migration accompanying the transient heat transfer can produce an undesired variation of product quality and even the so-called “silo rain”. The present work focuses on the systematic study of the transport of heat and moisture during the storage of granular materials in silos by developing the respective models on the basis of volume-averaging techniques. Transient heat transfer in such systems is studied in depth since it is the driving mechanism for natural convection and other transport processes. The parameters influencing heat transfer and natural convection are identified as the porous media modified Rayleigh number and the cylinder aspect ratio. The influence of these parameters is analyzed numerically and the model is validated by experiments. The dependence of natural convection on the parameters is discussed and a criterion for neglecting its influence on heat transfer is proposed. Furthermore, the simultaneous mass and heat transfer in warm and still moist materials stored in a silo with different hygroscopic activities is studied. Relevant equations for the modeling of such phenomena are proposed and dimensionless parameters governing the transport mechanism such as the porous media modified Lewis number, initial moisture content and the adsorption parameter besides Rayleigh number are identified. Simulations reveal the role of those parameters on the transport and accumulation of moisture. Natural convection is found to be the most influential mechanism in the creation of moisture mal-distribution and in the appearance of silo rain. Hygroscopic activity and initial moisture content of the material play also an important role in the migration of moisture as regulators of the availability of moisture in a system undergoing temperature gradients.