Direct laser slab face-cooling by a fluid crossing the main and pump laser beams is an important method to reach high average laser powers. However, the flow regime is usually maintained at low Reynolds numbers, to prevent the onset of turbulence features in the flow, that would degrade wavefront quality. We show here how bringing the fluid temperature to the thermooptical null point, close to the water/ice transition in the case of water, allows one to mitigate the optical consequences of hydrodynamic instabilities, by bleaching optically the temperature inhomogeneities within the flow. This optical process, dubbed index-leveling, opens the door to a highly efficient forced-flow, weakly turbulent face-cooling regime that should be instrumental to boost the kilowatt capabilities of next generation highpower lasers.