A thermal interposer is provided for attachment to the back surface of a semiconductor device so as to give a very low thermal resistance. In one preferred embodiment, the thermal interposer has two plates containing wick structures such as grooves. The thermal interposer is integrated with a semiconductor device so as to form a vapor chamber. In particular, the back surface of the semiconductor chip is in direct contact with the interior sealed volume of the vapor chamber, so as to greatly reduce the thermal resistance from the combination of the chip and the vapor chamber. Further, the upper plate is thermally coupled to a heat-sinking fixture such as a heat sink or a cold plate.