The interaction of a uniform cooling rate at the lake surface with sloping bathymetry efficiently drives cross-shore water exchanges between the shallow littoral and deep interior regions. The faster cooling rate of the shallows results in the formation of density-driven currents, known as thermal siphons, that flow downslope until they intrude horizontally at the base of the surface mixed layer. Existing parameterizations of the resulting buoyancy-driven cross-shore transport assume calm wind conditions, which are rarely observed in lakes and thereby restrict their applicability. Here, we examine how moderate winds (less than or similar to 5 m s(-1)) affect this convective cross-shore transport. We derive simple analytical solutions that we further test against realistic three-dimensional numerical hydrodynamic simulations of an enclosed stratified basin subject to uniform and steady surface cooling rate and cross-shore winds. We show cross-shore winds modify the convective circulation, stopping or even reversing it in the upwind littoral region and enhancing the cross-shore exchange in the downwind region. The analytical parameterization satisfactorily predicted the magnitude of the simulated offshore unit-width discharges in the upwind and downwind littoral regions. Our scaling expands the previous formulation to a regime where both wind and buoyancy forces drive cross-shore discharges of similar magnitude. This range is defined by the non-dimensional Monin-Obukhov length scale, chi(MO): 0.1 less than or similar to chi(MO) less than or similar to 0.5. The information needed to evaluate the scaling formula can be readily obtained from a traditional set of in situ observations.