Carbon/C3N heteronanotubes (CC3NNTs) have garnered significant interest for their distinctive performance and versatility across various applications. However, the understanding of interfacial heat transport within these heterostructures remains limited. This study aims to enrich the field by constructing models of CC3NNTs through the bonding of CNTs and C3NNTs, and employs nonequilibrium molecular dynamics (NEMD) simulations to predict their heat flux and thermal rectification (TR) effects. Placing the heat source in the CNT region induces a stronger heat flux compared to the C3NNT region, thus demonstrating a pronounced TR effect. This effect can be attributed to the mismatch in phonon spectra, as evidenced by the cumulative correlation factor derived from the phonon density of states (phonon DOS). Using this approach, we predict that the TR ratio for zigzag CC3NNTs (ZCC(3)NNT) significantly exceeds that of armchair CC3NNTs (ACC(3)NNT). Notably, in contrast to ACC(3)NNT, ZCC(3)NNT exhibits the phenomenon of negative differential thermal resistance in the backward heat flux with a temperature difference of Delta = 120 K. This phenomenon can be attributed to a lower phonon participation ratio at Delta = 120 K compared to other values of Delta. Subsequently, given that ZCC(3)NNT demonstrates the most pronounced TR ratio at room temperature, we explored how stress-strain, system size, defect density, and interface position impact the TR ratio. These insights are invaluable for guiding the design of thermal rectifiers, smart thermal management systems, and microelectronic processor coolers.