In this paper, we study temperature-constrained realtime 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. As example, we adopt a simple reactive speed control technique. We show how this simple reactive scheme can improve the processor utilization compared with any constantspeed scheme.