Microelectronic assemblies, and related devices and methods, are disclosed herein. For example, in some embodiments, a microelectronic assembly may include a package substrate having a surface; a die having a first surface and an opposing second surface, wherein the first surface of the die is coupled to the surface of the package substrate; and a cooling apparatus that may include a conductive base having a first surface and an opposing second surface, wherein the first surface of the conductive base is in thermal contact with the second surface of the die, and a plurality of conductive structures on the second surface of the conductive base, wherein an individual conductive structure of the plurality of conductive structures has a width between 10 microns and 100 microns.