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Die-temperature control to avoid hotspots is increasingly critical in multiprocessor systems-on-chip (MPSoCs) for stream computing. In this context, thermal balancing policies based on task migration are a promising approach to redistribute power dissipation and even out temperature gradients. Since stream computing applications require strict quality of service and timing constraints, the real-time performance impact of thermal balancing policies must be carefully evaluated. In this paper, we present the design of a lightweight thermal balancing policy MiGra, which bounds on-chip temperature gradients via task migration. The proposed policy exploits run-time temperature as well as workload information of streaming applications to define suitable run-time thermal migration patterns, which minimize the number of deadline misses. Furthermore, we have experimentally assessed the effectiveness of our thermal balancing policy using a complete field-programmable-gate-array-based emulation of an actual three-core MPSoC streaming platform coupled with a thermal simulator. Our results indicate that MiGra achieves significantly better thermal balancing than state-of-the-art thermal management solutions while keeping the number of migrations bounded.