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Next-generation multi-core multiprocessor real-time systems consume less energy at the cost of increased power density. This increase in power-density results in high heat density and may affect the reliability and performance of real-time systems. Thus, incorporating maximum temperature constraints in scheduling of real-time task sets is an important challenge. This paper investigates thermal-constrained energy-aware partitioning of periodic real-time tasks in heterogeneous multi-core multiprocessor systems. We adopt a power model which considers the impact of temperature and voltage on a processor's static power consumption. Two types of thermal models are used to respectively capture negligible and non-negligible amount of heat transfer among cores. We develop a novel genetic-algorithm based approach to solve the heterogeneous multi-core multiprocessor partitioning problem. Extensive simulations were performed to validate the effectiveness of the approach. Experimental results show that integrating a worst-fit based partitioning heuristic with the genetic algorithm can significantly reduce the total energy consumption of a heterogeneous multi-core multiprocessor real-time system.