An integrated circuit package includes a first die and second die above a substrate, and a vapor chamber above at least one of the first and second die. A vapor space within the vapor chamber is separated into at least a first section and a second section. The first section may be over the first die, and the second section may be over the second die, for example. The structure separating the first and second sections at least partly restricts flow of vapor between the first and second sections, thereby preventing or reducing thermal cross talk between the first and second dies. In some cases, an anisotropic thermal material is above one of the first or second die, wherein the anisotropic thermal material has substantially higher thermal conductivity in a direction of a heat sink than a thermal conductivity in a direction of a section of the vapor chamber.