Die-temperature control to avoid hotspots is increasingly critical in Multiprocessor System-on-Chip (MPSoCs) for stream computing. In this context, thermal balancing policies based on task migration are a promising approach to re-distribute 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 (FPGA)-based emulation of an actual 3-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.