Flip chip packages are described that include two or more thermal interface materials (TIMs). A die is mounted to a substrate by solder bumps. A first TIM is applied to the die, and has a first thermal resistance. A second TIM is applied to the die and/or the substrate, and has a second thermal resistance that is greater than the first thermal resistance. An open end of a heat spreader lid is mounted to the substrate such that the die is positioned in an enclosure formed by the heat spreader lid and substrate. The first TIM and the second TIM are each in contact with an inner surface of the heat spreader lid. A ring-shaped stiffener may surround the die and be connected between the substrate and heat spreader lid by the second TIM.