We used a set of large-eddy simulations to investigate the effect of one-dimensional stripe-like surface heat-flux heterogeneities on mixed-layer top entrainment. The profiles of sensible heat flux and the temporal evolution of the boundary-layer depth revealed decreased entrainment for small heat-flux amplitudes and increased entrainment for large heat-flux amplitudes, compared to the homogeneously-heated mixed layer. For large heat-flux amplitudes the largest entrainment was observed for patch sizes in the order of the boundary-layer depth, while for significantly smaller or larger patch sizes entrainment was similar as in the homogeneous case. In order to understand the underlying physics of this impact, a new approach was developed to infer local information on entrainment by means of the local flux divergence. We found an entrainment maximum over the centre of the stronger heated surface patch, where thermal energy is accumulated by the secondary circulation (SC) that was induced by the surface heterogeneity. Furthermore, we observed an entrainment maximum over the less heated patch as well, which we suppose is to be linked to the SC-induced horizontal flow convergence at the top of the convective boundary layer (CBL). For small heat-flux amplitudes a counteracting effect dominates that decreases entrainment, which we suppose is the horizontal advection of cold air in the lower, and warm air in the upper, CBL by the SC, stabilizing the CBL and thus weakening thermal convection. Moreover, we found that a mean wind can reduce the heterogeneity-induced impact on entrainment. If the flow is aligned perpendicular to the border between the differentially-heated patches, the SC and thus its impact on entrainment vanishes due to increased horizontal mixing, even for moderate wind speeds. However, if the flow is directed parallel to the border between the differentially-heated patches, the SC and thus its impact on entrainment persists.