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In many real-time systems, continuous operation can raise processor temperature, potentially leading to system failure, bodily harm to users, or a reduction in the functional lifetime of a system. Static power dominates the total power consumption, and is also directly proportional to the operating temperature. This reduces the effectiveness of frequency scaling and necessitates the use of sleep states. In this work, we explore the relationship between energy savings and system temperature in the context of fixed-priority energy-saving schedulers, which utilize a processor’s deep-sleep state to save energy. We derive insights from a well-known thermal model, and are able to identify proactive design choices which are independent of system constants and can be used to reduce processor temperature. Our observations indicate that, while energy savings are key to lower temperatures, not all energy-efficient solutions yield low temperatures. Based on these insights, we propose the SysSleep and ThermoSleep algorithms, which enable a thermally-effective sleep schedule. We also derive a lower bound on the optimal temperature achievable by energy-saving schedulers. Additionally, we discuss partitioning and task phasing techniques for multi-core processors, which require all cores to synchronously transition into deep sleep, as well as those which support independent deep-sleep transitions. We observe that, while energy optimization is straightforward in some cases, the dependence of temperature on partitioning and task phasing makes temperature minimization non-trivial. Evaluations show that compared to the existing purely energy-efficient design methodology, our proposed techniques yield lower temperatures along with significant energy savings.