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In this paper, we propose PROMETHEUS, a framework for proactive temperature aware scheduling of embedded workloads on single instruction set architecture heterogeneous multiprocessor systems-on-chip. It systematically combines temperature aware task assignment, task migration, and dynamic voltage and frequency scaling. PROMETHEUS is based on our novel low overhead temperature prediction technique, Tempo. In contrast to previous work, Tempo allows accurate estimation of potential thermal effects of future scheduling decisions without requiring any runtime adaptation. It reduces the maximum prediction error by up to an order of magnitude. Using Tempo, PROMETHEUS framework provides two temperature aware scheduling techniques that proactively avoid power states leading to future thermal emergencies while matching the performance needs to the workload requirements. The first technique, TempoMP, integrates Tempo with an online multiparametric optimization method to guide decisions on task assignment, migration, and setting core power states in a temperature aware fashion. Our second scheduling technique, TemPrompt uses Tempo in a heuristic algorithm that provides comparable efficiency at lower overhead. On average, these two techniques reduce the lateness of the tasks by 2.5× and energy-lateness product (ELP) by 5× compared to the previous work.