Performance of a task running on a many-core with distributed shared Last-Level Cache (LLC) strongly depends on two factors: the power budget needed to guarantee thermally safe operation and the LLC latency. The task’s thread-to-core mapping determines both the factors. Arrival and departure of tasks on a many-core deployed in an open system can change its state significantly in terms of available cores and power budget. Task migrations can thereupon be used as a tool to keep the many-core operating at the peak performance. Furthermore, the relative impacts of power budget and LLC latency on a task’s performance can change with its different execution phases mandating its migration on-the-fly.We propose the first run-time algorithm PCMig that increases the performance of a many-core with distributed shared LLC by migrating tasks based on their phases and the many-core’s state. PCMig is based on a performance-prediction model that predicts the performance impact of migrations. PCMig results in up to 16 % reduction in the average response time compared to the state-of-the-art.