Along with the performance improvement in state-of-art microprocessors, power densities are rising rapidly due to the fact that feature size scales faster than voltages [113]. In the last 5 years, though the processor frequency has only improved by 30%, the power density is more than doubled and expected to reach over 250 W/cm 2 [32]. Since energy consumption is converted into heat dissipation, high heat flux increases the on-chip temperature. The "hot spot" on current microprocessor die, caused by nonuniform peak power distribution, could reach up to 120 • C [14]. This trend is observed in both desktop and embedded processors [127, 158].Thermal increase will lead to reliability and performance degradation since CMOS carrier mobility is dependent on the operating temperature. High temperature can result in more frequent transient errors or even permanent damage. Industrial studies have shown that a small difference in operating temperature (10-15 • C) can make 2 times difference in the device lifespan [127]. Yeh et al. [150] also estimate that more than half of the electronic failures are caused by over-heated circuits. Furthermore, leakage power is exponentially proportional to temperature, which potentially results in more thermal runaway [141]. Studies also show that cooling cost increases super-linearly with the thermal dissipation [39].Since high on-chip thermal dissipation has severe detrimental impact, we have to control the instantaneous temperature so that it does not go beyond a certain threshold. Thermal management schemes at all levels of system design are widely studied for general-purpose systems. However, in the context of embedded systems, traditional packaging and cooling solutions are not applicable due to the limits on device size and cost. Moreover, embedded systems normally have limited energy budgets. Multitasking systems with real-time constraints add another level of difficulty since tasks have to meet their deadlines. Since such systems normally have well-defined functionality, this multi-objective problem admits design-time algorithms.DVS is acknowledged as one of the most efficient techniques both in energy optimization [21] and temperature management [158]. In existing literatures, temperature (energy)-constrained means that there is a temperature threshold W. Wang et al., Dynamic Reconfiguration in Real-Time Systems: Energy, Performance, and Thermal Perspectives, Embedded Systems, DOI 10.1007/978-1-4614-0278-7 7, © Springer Science+Business Media New York 2013 165 166 7 Temperature-and Energy-Constrained Scheduling(energy budget) which cannot be exceeded, while temperature (energy)-aware means that there is no constraint but maximum instantaneous temperature (total energy consumption) needs to be minimized. In this chapter, we examine a formal method based on model checking for temperature-and energy-constrained (TCEC) scheduling problems in multitasking systems. The classical timed automata [1] is extended with notions of task scheduling, voltage scaling, system temperature and ene...