A method and an apparatus for the efficient transfer of heat utilizing micro heat pipes that include a cellular foam or interconnected cellular/truss network having hollow ligaments. A predetermined fraction of the internal volume of the hollow ligaments is filled with a carefully chosen working fluid, and the ends of the hollow ligaments are sealed. In operation, the working fluid evaporates in the region of high heat flux and condenses in regions of lower temperature, resulting in the transfer or redistribution of the fluid's latent heat of vaporization. For open cell foams and interconnected networks, a second fluid flowing through the open cells, separate from the working fluid but also in thermal contact with the hollow ligaments, assists in the transfer of heat from the foam and networks.