As feature sizes decrease, power dissipation and heat generation density exponentially increase. Thus, temperature gradients in Multiprocessor Systems on Chip (MPSoCs) can seriously impact system performance and reliability. Thermal balancing policies based on task migration have been proposed to modulate power distribution between processing cores to achieve temperature flattening. However, in the context of MPSoC for multimedia streaming computing, where timeliness is critical, the impact of migration on quality of service must be carefully analyzed. In this paper we present the design and implementation of a lightweight thermal balancing policy that reduces on-chip temperature gradients via task migration. This policy exploits run-time temperature and load information to balance the chip temperature. Moreover, we assess the effectiveness of the proposed policy for streaming computing architectures by analyzing deadlines misses and architectural thermal effects of task migration using a cycle-accurate thermal-aware emulation infrastructure. Our results using a real-life software defined radio multitask benchmark show that our policy achieves thermal balancing while keeping migration costs bounded.