Sea ice leads play an important role in energy exchange between the ocean and atmosphere in polar regions, and therefore must be considered in weather and climate models. As sea ice leads are not explicitly resolved in such models, lead-averaged surface heat flux is of considerable interest for the parameterization of energy exchange. Measurements and numerical studies have established that the lead-averaged surface heat flux depends not only on meteorological parameters, but also on lead width. Nonetheless, few studies to date have investigated the dependency of surface heat flux on lead width. Most findings on that dependency are based on observations with lead widths smaller than a few hundred meters, but leads can have widths from a few meters to several kilometers. In this parameter study, we present the results of three series of large-eddy simulations of turbulent exchange processes above leads. We varied the lead width and air temperature, as well as the roughness length. As this study focused on conditions without background wind, ice-breeze circulation occurred, and was the main driver of the adjustment of surface heat flux. A previous large-eddy simulation study with uncommonly large roughness length found that lead-averaged surface heat flux exhibited a distinct maximum at lead widths of about 3 km, while our results show the largest heat fluxes for the smallest leads simulated (lead width of 50 m). At more realistic roughness lengths, we observed monotonously increasing heat fluxes with increasing lead width. Further, new scaling laws for the ice-breeze circulation are proposed.