The present paper reports numerical results of natural convection within an air filled square cavity with its horizontal walls submitted to different heating models. The temperature of the bottom horizontal surface (hot temperature) is maintained constant, while that of the opposite surface (cold temperature) is varied sinusoidally with time. The parameters governing the problem are the amplitude and the period of the variable temperature, the Rayleigh number and the Prandtl number. In constant cooling conditions, up to three different solutions (monocellular flow MF, bicellular vertical flow BVF and bicellular horizontal flow BHF) are obtained. Their existence ranges are delineated and the transitions observed are identified and described. In the variable cooling conditions, the effect of the amplitude and the period of the exciting temperature on heat transfer are examined in the case of the MF and BHF. In comparison with the constant heating conditions, it is found that the variable cooling temperature could lead to a resonance phenomenon characterized by an important increase in heat transfer by about 46.1 %.