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In this paper, we study temperature-constrained real-time systems, where real-time guarantees must be met without exceeding safe temperature levels within the processor. We give a short review on temperature issues in processors and describe how speed control can be used to trade off task delays against processor temperature. In this paper, we describe how traditional worst-case execution scenarios do not apply in temperature-constrained situations. We develop a delay computation methodology that can be used in combination with a simple reactive speed control technique, and show how this simple reactive scheme can decrease the delay of tasks compared with any constant-speed scheme.