This study aims to minimize the peak temperature for pipelined multi-core systems while providing hard real-time guarantees. Periodic Thermal Management (PTM) is adopted to control the temperature by periodically switching each pipelined stage into a lower power mode. The Pay-Burst-Only-Once principle from Real-Time Calculus theory is used in reverse to transform real-time guarantees into the constraints of the PTM schemes applied to all stages. We systematically study the peak temperature under PTM and present two algorithms to calculate it with different levels of accuracy and speed. A greedy principle-based heuristic method is proposed to solve the peak temperature optimization problem. Experiments are conducted on an Intel processor with physical temperature sensors. The results demonstrate that our approaches optimize the peak temperature more effectively than the sub-deadline partition approach. Simulations for scenarios involving more stages reveal that the proposed algorithms are scalable with respect to the number of stages.