Hotspots occur frequently in 3D multi-core processors (3D-MCPs) and they can adversely impact system reliability and lifetime. Moreover, frequent occurrences of hotspots lead to more dynamic voltage and frequency scaling (DVFS), resulting in degraded throughput. Therefore, a new thermal-constrained task scheduler based on thermal-pattern-aware voltage assignment (TPAVA) is proposed in this paper. By analyzing temperature profiles of different voltage assignments, TPAVA pre-emptively assigns different operating-voltage levels to cores for reducing temperature increase in 3D-MCPs. Moreover, the proposed task scheduler integrates a vertical-grouping voltage scaling (VGVS) strategy that considers thermal correlation in 3D-MCPs. Experimental results show that, compared with two previous methods, the proposed task scheduler can respectively lower hotspot occurrences by 47.13% and 53.91%, and improve throughput by 6.50% and 32.06%. As a result, TPAVA and VGVS are effectively for reducing occurrences of hotspots and optimizing throughput for 3D-MCPs under thermal constraints.