Hotspots occur frequently in 3D multi-core processors (3D-MCPs), and they may adversely impact both the reliability and lifetime of a system. We present a new thermally constrained task scheduler based on a thermal-pattern-aware voltage assignment (TPAVA) to reduce hotspots in and optimize the performance of 3D-MCPs. By analyzing temperature profiles of different voltage assignments, TPAVA pre-emptively assigns different initial operating-voltage levels to cores for reducing temperature increase in 3D-MCPs. The proposed task scheduler consists of an on-line allocation strategy and a new voltage-scaling strategy. In particular, the proposed on-line allocation strategy uses the temperature-variation rates of the cores and takes into two important thermal behaviors of 3D-MCPs that can effectively minimize occurrences of hotspots in both thermally homogeneous and heterogeneous 3D-MCPs. Furthermore, a new vertical-grouping voltage scaling (VGVS) strategy that considers thermal correlation in 3D-MCPs is used to handle thermal emergencies. Experimental results indicate that, when compared to a previous online thermally constrained task scheduler, the proposed task scheduler can reduce hotspot occurrences by approximately 66% (71%) and improve throughput by approximately 8% (2%) in thermally homogeneous (heterogeneous) 3D-MCPs. These results indicate that the proposed task scheduler is an effective technique for suppressing hotspot occurrences and optimizing throughput for 3D-MCPs subject to thermal constraints.