We investigate under what conditions the present-day long wavelength anomalous elevation (~500 m) of the southern African Plateau can be attributed to Mesozoic plume events. The anomalous, long wavelength topography of the southern African Plateau cannot be easily explained by recent heating of the upper mantle, as opposed to other areas of the African Superswell, and geomorphological studies provide few hard constraints on the timing of the uplift. A Mesozoic origin for the plateau uplift is attractive in that southern Africa experienced several large magmatic events in the Mesozoic. We formulate numerical and scaling models to investigate if plume material ponded beneath cratonic lithosphere in the Mesozoic could produce 500 m of present-day elevation. We find that starting plume heads are ineffective at producing much long lasting uplift because the material spreads into a thin layer, tens of km thick. The ponded plume material also suppresses secondary convection by having a stable boundary at its base. Over time, heat continues to flow out of the top of the lithosphere, and a net imbalance of heat flow in the lithosphere develops, resulting in subsidence. Even after the plume material has cooled to the temperature of the mantle adiabat, secondary convection supplies less heat to the lithosphere than is lost upward by conduction. The cratonic lithosphere returns to its original thermal structure on a timescale of less than 200 m.y. Even two mantle starting plume heads, one at the time of Karoo volcanism (ca.183 Ma) and the other at the time of kimberlite eruption (ca. 80--90 Ma) in our models, cannot produce much (<200 m) of the present-day anomalous elevation. However, significant uplift can be generated by plume tails, provided they linger beneath the lithosphere for ~25--30 m.y., and if the uplift effects of Mesozoic plume heads and tails are considered together, then it is possible to account for ~500 m of present-day elevation. Consequently, a Mesozoic plume model for plateau uplift in southern Africa appears to be a viable model, if plume tails delivered heat to the southern African lithosphere over a period of 25 m.y. or more.