A semiconductor assembly includes a semiconductor device and a connecting structure. The semiconductor device includes an interconnect region over a semiconductor substrate and a pillar layer having a plurality of pillar contacts on the interconnect region. The pillar layer also includes a plurality of radial heat conductors that have at least a portion overlying a heat source that is within and overlies the semiconductor substrate. Each radial heat conductor extends a length radially from the heat source that is at least twice as great as the diameter of the pillars. The connecting structure includes a connecting substrate that supports a first corresponding pillar contact that is in contact with a first pillar contact of the plurality of pillar contacts. The first connecting structure further includes a heat conductor, supported by the substrate, in contact with a first radial heat conductor of the plurality of radial heat conductors.