An assembly includes at least one heat emitting device and a continuous conformal cooling structure adhering directly to and conforming with surfaces of at least a portion of the at least one heat emitting device. The cooling structure may include a thermally-conductive, electrically-insulative layer adhering directly to surfaces of the at least one heat generating device to provide an electrically nonconductive, continuous, conformal layer covering all such surfaces. An inner metallization layer may be adhered directly to surfaces of at least a portion of the insulative layer. An outer metallization layer may be adhered directly to surfaces of the inner metallization layer to provide a thermally conductive layer covering such surfaces.