We consider the problem of energy-optimally mapping a set of moldable-parallel tasks in the steady-state pattern of a software-pipelined streaming computation onto a generic many-core CPU architecture with a 2D mesh geometry, where the execution voltage and frequency levels of the cores can be selected dynamically from a given set of discrete DVFS levels. We extend the Crown Scheduling technique for parallelizable tasks to temperature-aware scheduling, taking into account the tasks’ heat generation, the heat limit for each core, and the heat diffusion along the 2D mesh geometry of typical many-core CPU architectures. Our approach introduces a systematic method for alternating task executions between disjoint “buddy” core groups in subsequent iterations of crown schedules to avoid long-time overheating of cores. We present two integer linear program (ILP) solutions with different degrees of flexibility, and show that these can be solved for realistic problem sizes with today’s ILP solver technology. Experiments with several streaming task graphs derived from real-world applications show that the flexibility for the scheduler can be greatly increased by considering buddy-cores, thus finding feasible solutions in scenarios that could not be solved otherwise. We also present a fast heuristic for the same problem.