This paper presents the results of a numerical simulation for the natural convection inside an enclosure that has an inner open square at its center. The inner square is open at the top and connected to the ceiling of the enclosure. The open inner square distorts the convection patterns, slows down the flow, and provides a compartment to confine the fluid at the core of the enclosure. Ultimately, this lowers the local Nusselt number, Nu, along the hot wall, and reduces the heat flux through the enclosure. The analysis shows the effects of changing the dimensions of the inner square on the heat flux through the enclosure for a range of Rayleigh numbers- from 103 to 106. Short-sided inner squares work as flow deflectors while long-sided inner squares provide compartments to accommodate new flow circulation at the core of the enclosure. The inner square is most effective when the length of its sides equals the width of the stagnant core inside the empty enclosure at the same Rayleigh number, and the heat flux at this condition is the lowest. Inner squares made of thermally conducting materials can reduce the heat flux through the enclosure by 70%, while adiabatic inner squares can reduce the heat flux by 90%. Inner squares reduce the external heat load on buildings when fitted inside the holes of hollow bricks used in building facades. The external heat flux can be lowered by 30%–55% depending on the material of the inner square and outer side temperature.