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Multi-core System-on-Chip (SoC) has become a popular execution platform for many embedded real-time systems that require high performance and low power-consumption. High temperature is known to accelerate the failure of deep submicron chips. To prevent such accelerated failures due to chip overheating, various thermal-aware scheduling (TAS) algorithms and dynamic thermal management (DTM) have been proposed and applied to mission/safety-critical applications. To control on-chip temperature more effectively, it is necessary to predict the thermal dynamics of a multi-core chip in real time and trigger appropriate power/temperature management before overheating the chip. However, due to dynamically-changing runtime environments, it is very difficult to estimate the chip temperature on-the-fly. In this paper, we propose models of efficiently estimating multi-core chip temperature while accounting for the system dynamics in real time. Based on these models, we design a proactive peak temperature manager (PTM) which periodically estimates future core temperature and triggers proper DTMs on the estimated-to-be-overheated cores for their cooling without violating applications timing constraints. Our in-depth evaluation based on the HotSpot thermal simulator has shown that the proposed method can predict the occurrence of peak temperature in a core with 90-98% accuracy, and using the estimated thermal model of a multi-core chip, PTM can effectively keep core temperature below a given threshold without violating any timing constraint.