In this article, the authors numerically investigate dynamic heat transfer related to free convection in porous and partially porous cavities, paying particular attention to the dependence of velocity and temperature fields on Rayleigh (Ra) number, porous layer permeability, and cavity aspect ratio (AR), the ratio between its height and width. Heat and fluid flows inside the cavity are described by using the generalized porous medium model, and the governing equations were numerically solved using the artificial compressibility version of the characteristic-based split scheme. The proposed model was first applied to the simulation of heat and fluid flows in a square porous cavity, and an excellent agreement was found between the results obtained and the data available in the literature. The analysis was then extended, here for the first time, to transient natural convection in partly porous cavities, with AR equal to 4:1 and 8:1 for different Ra and Darcy (Da) numbers. The mean Nusselt (Nu) number was calculated as a function of cavity geometrical characteristics, porous layer permeability, and fluid properties.