A multi-chip package includes multiple IC die interconnected to a package substrate. An integrated heat spreader (IHS) is located over one or more primary IC die, but is absent from over one or more secondary IC die. Thermal cross-talk between IC dies and/or thermal performance of individual IC dies may be improved by constraining the dimensions of the IHS to be over less than all IC die of the package. A first thermal interface material (TIM) may be between the IHS and the primary IC die, but absent from over the secondary IC die. A second TIM may be between a heat sink and the IHS and also between the heat sink and the secondary IC die. The heat sink may be segmented, or have a non-planarity to accommodate differences in z-height across the IC die and/or as a result of constraining the dimensions of the IHS to be over less than all IC die.