In addressing climate change, there exists a vertical inter-generational coordination challenge that necessitates determining the extent of costs current generations are willing to bear to prevent potential future climate damages. This question involves balancing contemporary interests with those of future generations, requiring careful trade-offs between present mitigaation costs and projected future climate losses. As part of the theoretical series on “time–space–effect–benefit” in carbon mitigation, this chapter specifically focuses on temporal coordination. We construct an inter-temporal equilibrium pathway by establishing a moderate yet proactive discount rate framework, thereby harmonizing current mitigation costs with future climate damages. This approach addresses fundamental questions regarding the inter-temporal allocation of mitigation responsibilities and cost distribution while providing methodological foundations for coordinating long- and short-term emission reduction strategies. The developed framework advances the discourse on inter-generational equity in climate governance through its systematic integration of equilibrium pathway modeling and discount rate determination, offering practical insights for balancing temporal dimensions in climate policy-making.