A heat dissipating structure includes: a heat spreader; and a plurality of compliant beams attached to the heat spreader. The beams are formed of a high-conductive material such that a maximum stress of each beam is less than a fatigue stress of the high-conductive material; said beams are placed at an angle relative to a chip surface such that the beams are able to exert bending compliance in response to x, y, and z forces exerted upon them. The structure also includes a thermal material interface for bonding said structure to the chip surface. Both the heat spreader and the compliant beams can be machined from a copper block. An alternative heat dissipating structure includes compliant beams soldered to the chip surface.