An apparatus for cooling an electronic component has a planar top member of a thermal energy conductive material and a parallel planar bottom member of the material, the planar bottom member including a surface having regions configured for heat exchange contact with the electronic component. The joined planar top and bottom members have a sidewall structure of reduced height (and generally the height of the cold plate) between active areas in order to improve flexibility. The stiffness of the sidewalls is reduced by very advantageously reduce the height of the sidewalls. In one embodiment, the sidewalls are shorter in height corresponding to regions only between active areas. Alternatively, the sidewalls are of reduced height everywhere by insetting the active areas within the top and/or bottom sheets.