A method for forming a semiconductor die package is provided. The method includes bonding a first semiconductor die and a second semiconductor die to a package substrate; disposing a lid structure over the package substrate and over the first and second semiconductor dies, wherein the lid structure has a first opening exposing the second semiconductor die; attaching the lid structure to the first semiconductor die using a first thermal interface material (TIM) layer; disposing a heat sink over the lid structure, wherein the heat sink has a first portion located over the lid structure, and a second portion extending into the first opening of the lid structure; and attaching the second portion of the heat sink to the second semiconductor die using a second TIM layer, wherein the first TIM layer has a thermal conductivity higher than a thermal conductivity of the second TIM layer.