In the present study, thermal-fluid behaviors in a rectangular enclosure of width-to-height aspect ratio 4:1 heated from below with wall-temperature varied sinusoidally in ti-me is investigated numerically. The main concerns are the effects of the wall-heating modulation on the threshold of thermal instability and the oscillatory cellular convection heat transfer performance at the post-critical conditions. For investigation of heating modulation effects at various conditions, inclination of the enclosure is also considered. The results demonstrate that a bottom-wall temperature modulation of larger amplitude and/or lower frequency generates a relatively stabilizing effect. The trend is the same as those claimed in the previous linear stability analyses of infinite horizontal fluid layer. However, the present numerical solutions further disclosed more detailed information about the flow structure as well as the local heat transfer performance, which are useful in understanding of the modulation mechanisms.