A workpiece stack-up that includes at least a steel workpiece and an aluminum-based workpiece can be resistance spot welded by a spot welding method in which the welding current is controlled to perform one or more stages of weld joint development. When it is desired to terminate weld current flow and to solidify a liquid weld pool into a weld nugget (of mostly aluminum-based composition), additional cooling is applied to the outer surface of the aluminum-based workpiece around the contact area of the spot welding electrode engaging the surface of the aluminum-based workpiece surface. The additional cooling is applied and controlled so as to increase the rate of solidification of the liquid aluminum-based material and to control the direction of solidification of the weld nugget to better confine impurities, and the like, originally in the melt, at the surface of the steel workpiece.