As the demand for ocean exploration grows, nuclear reactors utilizing natural circulation for power generation have become a significant propulsion force for long-term operations. However, the coolant within the reactor system is influenced by ocean conditions, characterized by passive flow fluctuations. In this study, a onedimensional (1D)/three-dimensional (3D) coupling analysis method is developed and applied to investigate the impact of heaving conditions on the flow and heat transfer performance of natural circulation with a narrow rectangular channel. The flow and heat transfer characteristics within the narrow rectangular channel, which represents the reactor core, are analyzed in detail using a three-dimensional approach, while the overall natural circulation performance of the system is assessed using a one-dimensional method. Validation is conducted based on pulsating flow experiments and natural circulation experiments. Subsequently, detailed thermal-hydraulic parameters for both the rectangular channel and the natural circulation system are obtained. The results indicate that flow fluctuations caused by the heaving conditions significantly influence the transient performance of both the rectangular channel and the entire natural circulation system. However, the time-averaged flow resistance and heat transfer capability remain unaffected by the heaving conditions. An increase in the heaving period results in a decrease in flow fluctuations within the natural circulation system, and the phase delay between heaving displacement and mass flow flux also diminishes. Conversely, as the heaving amplitude increases, flow fluctuations rise, but this has no effect on the phase delay. Due to the ring effect introduced by the heaving motion, the difference between the main flow zone and the wall zone dominates the transient thermal-hydraulic performance in the narrow rectangular channel. Additionally, the heaving motion does not significantly influence the cycle-averaged flow resistance or the cycle-averaged Nusselt number.