A heat spreader or lid for a microelectronic package, in which the heat spreader has an underside surface that includes at least one curvilinear contour, in which the curvilinear contour is selected from at least one positive or protruding curvilinear feature, at least one negative or recessed curvilinear feature, and a combination thereof. A microelectronic package that includes the heat spreader/lid, in which there is improved heat dissipation or reduced mechanical stress in an interface between the heat spreader/lid and a circuit chip.