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The relentless advancement of hybrid-electric technologies in aviation, coupled with the dynamic evolution of space exploration driven by the new space economy, underscores the criticality of thermal design in aerospace systems. In the context of hybrid-electric aircraft, managing temperature fluctuations introduced by high-power components and energy storage systems is of paramount importance to guarantee safety and performance. Furthermore, in space exploration, maintaining thermal stability is crucial, as temperature fluctuations can significantly impact the precision of scientific instruments and the structural integrity of spacecraft. The need for precise temperature control, innovative cooling strategies, and resilient thermal barrier materials is evident. Founded on three pivotal pillars, this proposal is for an exploratory study into a radical new multidisciplinary approach to the problem of aerospace thermal design and management. The first pillar of AMPERE focuses on developing advanced multi-scale models capable of capturing the complexities of heat storage and transmission across diverse scales. From macroscopic structures to molecular interactions, these models bridge the gap between classical thermal transfer approaches and modern physics. The second pillar revolves around the creation of cutting-edge multi-physics models, grounded in unified structural theories and higher-order finite elements. This approach aims to consider intricate interplays between structural stability, material properties, and various physical fields, including thermal, electrical, magnetic, and chemical. Based on the innovative simulation methods and digital twins of dedicated aerospace systems, the third pillar centers on engineering thermal design and management solutions, to finally meet societal needs beyond current technological limitations, providing unprecedent innovative control methods, smart devices, optimization strategies for energy storage systems, and thermal barriers optimization for future aircraft and spacecraft.