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Power and temperature are key design concerns in modern computing systems. Power minimization is essential for battery-operated devices and for large-scale data center facilities. The spatial and temporal allocation of within-die power consumption lead to thermal gradients and hot spots during operation. Temperature impacts key circuit metrics such as reliability, speed, and leakage power, and it is a major constraint towards improving the performance of high-end computing devices. Due to the enormous complexities and sheer number of modeling parameters of state-of-the-art designs, pre-silicon power and thermal models cannot be trusted blindly. It is necessary to complement pre-silicon analysis with post-silicon thermal and power characterization on the fabricated devices, and then to use the characterization results to improve the design during re-spins before ramp and production. In this paper, we describe new techniques for thermal and power characterization of real computing devices. We show how the measurements from infrared imaging, embedded thermal sensors, and current meters can be integrated to accurately characterize the temperatures and power of computing devices during operation. We describe the key algorithmic and experimental techniques required to overcome the challenges encountered when working with real devices. We present characterization results of a dual-core processor and a programmable logic device.