Vertically-integrated 3D multiprocessors systems-on-chip (3D MPSoCs) provide the means to continue integrating more functionality within a unit area while enhancing manufacturing yields and runtime performance. However, 3D MPSoCs incur amplified thermal challenges that undermine the corresponding reliability. To address these issues, several advanced cooling technologies, alongside temperature-aware design-time optimizations and run-time management schemes have been proposed. In this monograph, we provide an overall survey on the recent advances in temperature-aware 3D MPSoC considerations. We explore the recent advanced cooling strategies, thermal modeling frameworks, design-time optimizations and run-time thermal management schemes that are primarily targeted for 3D MPSoCs. Our aim of proposing this survey is to provide a global perspective, highlighting the advancements and drawbacks on the recent state-of-the-art