This invention relates to cooling devices for multi-chip semiconductor devices, system-on-a-package devices, and other packaged devices. Because of the non-uniform height across the surface in such large-chip and multi-chip assemblies, providing heat exchange can be troublesome. Many air cooled heat sinks are too stiff to adapt to such non-uniform or warped shapes of chips or to shape-changing chip surfaces during operation. In the present disclosure, application of a mechanical load perpendicular to the chip plane causes certain features to flex and adapt to the non-uniform height of the chip plane, providing improved heat exchange.