Two factors primarily affect the performance of multi-threaded tasks on many-core processors with logically-shared and physically-distributed Last-Level Cache (LLC): the LLC latencies of threads running on different cores and the per-core power budgets that aim to guarantee thermally safe operation. Two knobs affect these factors: First, the mapping of threads to cores affects both the LLC latencies and the power budgets. Second, dynamic power budgeting refines the power budgets during task execution. A mapping that spatially distributes threads across the many-core increases the power budgets, but unfortunately also increases the LLC latencies. Contrarily, mapping all threads near the center of the many-core minimizes the LLC latencies, but unfortunately also decreases the power budgets. Consequently, both metrics cannot be simultaneously optimal, which leads to a Pareto-optimization for task mapping that has formerly not been exploited. Dynamic power budgeting reallocates the power budgets according to the tasks’ execution phases. This results in a dynamically changing non-uniform power budget, which further increases the performance. We are the first to present a run-time algorithm PCGov combining task-agnostic task mapping and task-aware dynamic power budgeting for many-cores with shared distributed LLC. PCGov yields up to 21 percent lower response time and 13 percent lower energy consumption compared to the state-of-the-art, with a low overhead of less than 0.5 percent.