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In this work we use the Fourier expansion to characterize and model many-core processor workloads for the purpose of computing accurate predictions of individual core thermal statuses. We demonstrate, that even if the workload is modeled with only a few components of its Fourier expansion, not only we obtain improved accuracy of aggregate performance measures like throughput or power consumption, but also we obtain highly accurate thermal profiles of individual cores. In this work we present the measurement and simulation results and accuracy analysis of our proposed approach. Our experiments show that assuming average activity of threads in a multi-threaded workload run on a many-core processor may lead to as much as 25% error in the estimation of the overall throughput of the system, and even larger discrepancies in the estimates of individual core's temperature traces, while applying even a few-component Fourier expansion of the benchmark traces reduce these errors by large margins.