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In this paper a precise formulation of the problem of minimizing the maximum completion time of tasks on a multi-core processor, subject to thermal constraints is presented. The power model used in this work, accounts for the leakage dependence on temperature, while the thermal model is based on the HotSpot model. The general problem is shown to be a non-linear optimization problem that includes cyclic constraints between temperature and power. The derived policy of dynamic frequency and voltage control results in a performance improvement of 19.6% over an optimal policy which performs speed-only control.