A device package and a method of forming a device package are described. The device package has dies disposed on a substrate, and one or more layers with a high thermal conductivity, referred to as the highly-conductive (HC) intermediate layers, disposed on the dies on the substrate. The device package further includes a lid with legs on an outer periphery of the lid, a top surface, and a bottom surface. The legs of the lid are attached to the substrate with a sealant. The bottom surface of the lid is disposed over the one or more HC intermediate layers and the one or more dies on the substrate. The device package may also include thermal interface materials (TIMs) disposed on the HC intermediate layers. The TIMs may be disposed between the bottom surface of the lid and one or more top surfaces of the HC intermediate layers.