A numerical study is performed for time-varying natural convection of an incompressible Boussinesq fluid in a sidewall-heated square cavity. The temperature at the cold sidewall T-c is constant but at the hot sidewall a time varying temperature condition is prescribed, T-H = <(T)over bar (H)> + Delta T'sin ft. Comprehensive numerical solutions are found for the time-dependent Navier-Stokes equations. The numerical results are analysed in detail to show the existence of resonance, which is characterized by maximal amplification of the fluctuations of heat transfer in the interior. plots of the dependence of the amplification of heat transfer fluctuations on the non-dimensional forcing frequency omega are presented. The failure of Kazmierczak & Chinoda (1992) to identify resonance is shown to be attributable to the limitations of the parameter values they used. The present results illustrate that resonance becomes more distinctive for large Ra and Pr similar to O(1). The physical mechanism of resonance is delineated by examining the evolution of oscillating components of flow and temperature fields. Specific comparisons are conducted for the resonance frequency omega(r) between the present results and several other previous predictions based on the scaling arguments.