The combined effects of natural convection and thermal radiation on heat transfer within an air-filled square cavity are investigated numerically. The cavity’s upper and lower walls are insulated, while its vertical walls are subjected to temperatures spatially varying in a sinusoidal manner. The thermal stratification evolution and fluid dynamic behavior in the enclosure are studied using the finite-difference method. A radiosity method is used to calculate the view factors, radiosity vector, and radiative heat exchange between cavity surfaces. The effects of Rayleigh number (Ra) and phase shift (ϕ) between the temperatures of hot and cold walls on the results are examined. It is shown that the increase in phase shift and Rayleigh number, in the presence of radiation, significantly enhances the heat transfer rate.