Weekly storage of coolness in heavy walls (walls with large thermal inertia or large characteristic time constants or low Fourier numbers) was investigated numerically by considering one-dimensional heat conduction through the walls. The study consisted of first analyzing the heat flow through a single wall and considering various boundary conditions on the inside. The boundary conditions were: constant inside air tempeture throughout the day, variable inside air temperature on a 24-hour cycle, and variable inside air temperature on a 48-hour cycle. Next, the heat flow through walls was studied through a thermal network analysis of a simple building. In this case it was assumed that the ambient air temperature (following a periodic distribution) was increased suddenly and followed this new distribution for many days thereafter. It was concluded that walls with high thermal inertia or time constant can store coolness for several days. The larger the time constant of the wall (for example adobe as compared with brick) the longer it takes for the wall temperature to reach a steady periodic distribution after the change has occurred. However, because of low thermal conductivity of adobe, the retrieval of the stored coolness in these walls is slow, and the mean daily temperature of the room air in the adobe building does not change appreciably beyond seven days after the change. Increase of the wall thickness beyond 50 cm does not improve the thermal performance of the building significantly.