In this article, we study the problem of how to maximize the throughput of a periodic real-time system under a given peak temperature constraint.We assume that different tasks in our system may have different power and thermal characteristics. Two scheduling approaches are presented. The first is built upon processors that can be in either active or sleep mode. By judiciously selecting tasks with different thermal characteristics as well as alternating the processor's active/sleep mode, the sleep period required to cool down the processor is kept at aminimum level, and, as the result, the throughput ismaximized.We further extend this approach for processors with dynamic voltage/frequency scaling (DVFS) capability. Our experiments on a large number of synthetic test cases as well as real benchmark programs show that the proposed methods not only consistently outperform the existing approaches in terms of throughput maximization, but also significantly improve the feasibility of tasks when a more stringent temperature constraint is imposed. © 2014 ACM.