An integrated circuit (IC) chip module includes a carrier, a stiffening frame, an IC chip, a first directional heat spreader, and a second directional heat spreader. Presented herein is a fabrication method that includes attaching the stiffening frame to the carrier. The stiffening frame includes a central opening, a base portion, a first pair of opposing sidewalls, and a second pair of opposing sidewalls. The method includes electronically coupling the semiconductor chip to the carrier concentrically arranged within the central opening. The method includes thermally contacting the first directional heat spreader to the semiconductor chip. The first directional heat spreader transfers heat from the semiconductor chip towards the first pair of opposing sidewalls. The method includes thermally contacting the second directional heat spreader to the first directional heat spreader. The second directional heat spreader transfers heat from the first directional heat spreader towards the second pair of opposing sidewalls.