Two factors primarily affect performance of multi-threaded tasks on many-core processors with both shared and physically distributed Last-Level Cache (LLC): the power budget associated with a certain task mapping that aims to guarantee thermally safe operation and the non-uniform LLC access latency of threads running on different cores. Spatially distributing threads across the many-core increases the power budget, but unfortunately also increases the associated LLC latency. On the other side, mapping more threads to cores near the center of the many-core decreases the LLC latency, but unfortunately also decreases the power budget. Consequently, both metrics (LLC latency and power budget) cannot be simultaneously optimal, which leads to a Pareto-optimization that has formerly not been exploited. We are the first to present a run-time task mapping algorithm called PCMap that exploits this trade-off. Our approach results in up to 8.6 % reduction in the average task response time accompanied by a reduction of up to 8.5 % in the energy consumption compared to the state-of-the-art.