Moisture is one of the key variables that must be considered when determining the load profiles that can be safely applied to a transformer. The presence of high amount of water accelerates the aging rate of the transformer's solid insulation, shortening the life expectancy of the equipment. Moreover, the dynamic processes of moisture migration between paper and oil must be considered in order to avoid a potential cause of failure, such as the formation of bubbles in the paper-oil interface, or the moisture saturation and the subsequent formation of liquid water in oil. These processes are linked to the changes in temperature; however, within the transformer, both processes have very different time constants, which complicates the analysis. In this paper, a mathematical model is presented, which allows us to study the moisture dynamics in a transformer. The model considers a multi-physical approach incorporating a thermal module and a moisture dynamic module that makes it possible to analyze the behavior of the moisture for a certain load profile. Some application cases are included in this paper to illustrate the model operation.