Semiconductor chip structures are provided with embedded thermal conductors for removing heat from one or more electrically conductive circuit members thereof, wherein the circuit members are formed on one or more dielectric layers above a substrate, each layer having a low dielectric constant and a low thermal conductivity. One or more cooling posts, for example, multiple thermally conductive plugs, are selectively disposed within the semiconductor chip structure adjacent to one or more electrically conductive members and thermally coupled thereto so that heat produced by the members is transferred into and through the cooling posts for forwarding to the substrate and/or to an upper surface of the semiconductor chip structure. The backside of the substrate has a thermal sink thermally coupled thereto and electrically isolated from the substrate. The thermal sink includes one or more thermally conductive via structures embedded within the substrate and aligned to thermally contact to the cooling posts disposed above the substrate.