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Thermal constraints have limited the performance improvement of modern computing systems in recent years. As a system could fail if the peak temperature exceeds its thermal constraint, overheating should be avoided while designing a system. Moreover, higher temperature also leads to higher leakage power consumption. This paper explores dynamic thermal management to minimize the energy consumption for a specified computing demand under the thermal constraint. We develop energy-efficient speed scheduling schemes for frame-based real-time tasks under thermal constraints. Experimental results reveal the effectiveness of the proposed scheme in terms of energy consumption in comparison with the reactive schemes in the literature.