A semiconductor device is made by forming a heat spreader over a carrier. A semiconductor die is mounted over the heat spreader with a first surface oriented toward the heat spreader. A first insulating layer is formed over the semiconductor die and heat spreader. A via is formed in the first insulating layer. A first conductive layer is formed over the first insulating layer and connected to the heat spreader through the via and to contact pads on the semiconductor die. The heat spreader extends from the first surface of the semiconductor die to the via. A second insulating layer is formed over the first conductive layer. A second conductive layer is electrically connected to the first conductive layer. The carrier is removed. The heat spreader dissipates heat from the semiconductor die and provides shielding from inter-device interference. The heat spreader is grounded through the first conductive layer.