Asymptotic and numerical methods are used to analyse periodically forced natural convection over slowly varying topography. This models the diurnal heating/cooling cycle in lakes and reservoirs. The asymptotic solution includes the effects of advection on the temperature. The asymptotic results are confirmed by the numerical results. The numerical results are also used to examine flow regimes where the asymptotic results break down. In particular, the presence of a vertical boundary leads to a permanent stratification in the deeper regions due to a nonlinear pumping process in the shallows. Heat transfer calculations and two limiting cases are also presented.