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In modern multi-core Mixed-Criticality (MC) systems, a rise in peak power consumption due to parallel execution of tasks with maximum frequency, specially in the overload situation, may lead to thermal issues, which may affect the reliability and timeliness of MC systems. Therefore, managing peak power consumption has become imperative in multi-core MC systems. In this regard, we propose an online peak power and thermal management heuristic for multi-core MC systems. This heuristic reduces the peak power consumption of the system as much as possible during runtime by exploiting dynamic slack and per-cluster Dynamic Voltage and Frequency Scaling (DVFS). Specifically, our approach examines multiple tasks ahead to determine the most appropriate one for slack assignment, that has the most impact on the system peak power and temperature. However, changing the frequency and selecting a proper task for slack assignment and a proper core for task re-mapping at runtime can be time-consuming and may cause deadline violation which is not admissible for high-criticality tasks. Therefore, we analyze and then optimize our run-time scheduler and evaluate it for various platforms. The proposed approach is experimentally validated on the ODROID-XU3 (DVFS-enabled heterogeneous multi-core platform) with various embedded real-time benchmarks. Results show that our heuristic achieves up to 5.25% reduction in system peak power and 20.33\% reduction in maximum temperature compared to an existing method while meeting deadline constraints in different criticality modes.