Implementing Multi-Processor-Systems-on-Chip (MPSoCs) in 3-Dimensional (3D) ICs has many benefits, but the increased power density can cause significant thermal problems, resulting in decreased reliability, lifetime and performance. This paper presents a fast thermal-aware approach for mapping throughput constrained streaming applications on a 3D MPSoC. While there are some published works on thermal-aware mapping of real-time applications, throughput constraints and data dependencies are mostly not considered. Further, conventional approaches have long running times due to slow iterative thermal simulations. In our approach, to avoid slow thermal simulations for every candidate mapping, a thermal model of the 3D IC is used to derive an on-chip power distribution that minimizes the temperature before the actual mapping is done. Next, this distribution is used in a resource allocation algorithm to derive a mapping that meets the throughput constraint while approaching the target power distribution and minimizing energy consumption. This way, in contrast to most existing approaches, a mapping can be derived in the order of minutes. Experiments show a 7% reduction in peak temperature and a 47% reduction in communication energy compared to mappings based on load balancing.