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Extracting high performance from multi-core processors requires increased use of thermal management techniques. In contrast to offline thermal management techniques, online techniques are capable of sensing changes in the workload distribution and setting the processor controls accordingly. Hence, online solutions are more accurate and are able to extract higher performance than the offline techniques. This paper presents performance optimal online thermal management techniques for multicore processors. The techniques include dynamic voltage and frequency scaling and task-to-core allocation or task migration. The problem formulation includes accurate power and thermal models, as well as leakage dependence on temperature. This paper provides a theoretical basis for deriving the optimal policies and computationally efficient implementations. The effectiveness of our DVFS and task-to-core allocation techniques are demonstrated by numerical simulations. The proposed task-to-core allocation method showed a 20.2% improvement in performance over a power-based thread migration approach. The techniques have been incorporated in a thermal-aware architectural-level simulator called MAGMA that allows for design space exploration, offline, and online dynamic thermal management. The simulator is capable of handling simulations of hundreds of cores within reasonable time.