This paper presents the results of a numerical study for using a simple insertion to reduce the heat transfer through an air-filled square cavity when subjected to a temperature gradient. The insertion is a rectangular sheet folded in a special way to produce the shape of a rotated letter G. The insertion is thermally conductive, and in perfect contact with the walls of the cavity. The cavity has thick conductive walls. The two outer vertical sides of the cavity are isothermal, and the two horizontal sides are adiabatic. The solution of continuity, momentum, and energy equations for this system yields the isotherms, streamlines, and heat flux transported across the cavity. The insertion suppresses the convection currents inside the cavity and hence reduces the heat transfer rate across them. The analysis shows the effect of the insertion dimensions and thermal properties on the heat transfer rate through the cavity. This paper also presents the results of using this insertion inside the holes of an ordinary building brick. The insertion is an easy tool to manufacture and a simple device to use for reducing the heat transfer through the blocks. The G insertion reduces the heat flux by 27–42%.