A semiconductor device thermal connection used to remove heat from a semiconductor device, such as an integrated circuit, includes a metallic barrier layer on the semiconductor device, and a high thermal conductivity material on the metallic barrier layer that joins the semiconductor device to a thermal heat spreader. The metallic barrier layer may be one or more sputtered layers, and the high thermal conductivity material may be a metallic material, for instance including indium, that is soldered onto the sputtered material. The high thermal conductivity material may form a primary thermal connection in conducting heat away from the semiconductor device. A secondary thermal connection may be made between the heat spreader and a heat sink. The secondary thermal connection may include a compressible solid carbon fiber material. A diaphragm may be used to contain the carbon fiber material, to prevent carbon fibers from coming into contact with the semiconductor device.