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We investigate autonomic power control policies for Internet servers and data centers. In particular, by monitoring the system load and thermal status, we decide how to vary the utilized processing resources to achieve acceptable delay and power performance. We formulate the problem using a dynamic programming approach that captures the power-performance tradeoff. We study the structural properties of the optimal solution and develop low-complexity justified heuristics, which achieve significant performance gains over standard benchmarks. The performance gains are higher when the load exhibits stronger temporal variations. We also demonstrate that the heuristics are very efficient, in the sense that they perform very close to the optimal solution obtained via dynamic programming.