The aspirated hypersonic air-breathing propulsion system requires a large amount of power generation, but its special structure makes it impossible to adopt common power generation methods. The high-temperature gaseous hydrocarbon fuel thermal power generation (TPG) system was developed to solve the power generation problem for hypersonic air-breathing propulsion system. But off-design operating conditions of the hypersonic propulsion system results in a more complex process for both propulsion system and the TPG system. To better analyzing the dynamic thermos-physical characteristics of hypersonic airbreathing propulsion system considering thermal-mechanical coupling process among cooling/TPG system, a dynamic analytical model was developed, and the dynamic thermos-physical characteristics of TPG system under different off-design working conditions were conducted. It can be concluded from the analytical results that the dynamic process of thermos-physical characteristics shows a complex trend under the flight Mach number and fuel equivalence ratio off-design working conditions. Such complexity of dynamic characteristics brings difficulties in fuel supply for the propulsion system.