According to an aspect of the disclosure, an example microelectronic device assembly includes a substrate, a microelectronic element electrically connected to the substrate, a stiffener element overlying the substrate, and a heat distribution device overlying the rear surface of the microelectronic element. The stiffener element may extend around the microelectronic element. The stiffener element may include a first material that has a first coefficient of thermal expansion (“CTE”). A surface of the stiffener element may face toward the heat distribution device. The heat distribution device may include a second material that has a second CTE. The first material may be different than the second material. The first CTE of the first material of the stiffener element may be greater than the second CTE of the second material of the heat distribution device.