The complexity of marine gas hydrate systems at the Peruvian convergent margin has been linked to the post-Miocene history of vertical tectonics and subduction erosion that affected the forearc. Here, multichannel seismic data and published findings reveal that such a complexity has been further extended by the occurrence of the pre-Miocene deep Morsa Norte Graben (MNG) off Trujillo (8°–9° S) in the Central Peru margin. At water depths of 650–750 m in the upper slope, directly above the MNG depocentre (which has a 4–6 km overburden thickness), continuous bottom-simulating reflections (BSRs) and concentrated sub-BSR high-amplitude reflections are confined beneath a layered basin with a low–moderate near-seafloor heat flow (7–33 mW m −2 ). A deeper BSR modelled with a thermogenic gas composition is associated with the enhanced reflections. At a water depth of 900 m, sub-BSR reflections become less frequent in an area with a layered sediment cover defined by a moderate near-seafloor heat flow (15–33 mW m −2 ). At a water depth of 1200 m, where the MNG is relatively thick (3–4 km overburden thickness), faults connect patchy BSRs with a moderate–high near-seafloor heat flow (52–110 mW m −2 ). There, sub-BSR enhanced reflections are scarce. Immediately above the top of the gas hydrate stability zone (GHSZ), the near-seafloor heat flow reaches 81 mW m −2 . Modelling suggests a water depth-dependent transport of heat towards the seafloor with respect to the top of the GHSZ, implying that the closer the seafloor is to the top of the GHSZ, the lower the advection of heat, and vice versa. Recent seafloor-related depositional and structural features amplify such relations in agreement with near-seafloor heat-flow variability. However, towards the area outside the extent of the MNG (<3 km overburden thickness), continuous BSRs are not linked either to a deeper BSR or to sub-BSR enhanced reflections. The continuity of one of these BSRs is deflected upwards beneath a slump, suggesting an incomplete thermal re-equilibration of the GHSZ. Therefore, we conclude that the BSR responds to: (1) the confinement and thickening of the free-gas zone (FGZ) above the MNG depocentre due to the sealing effect of recent sedimentation close to the top of the GHSZ; (2) the seepage of gas-rich fluids from a thinned FGZ above the relatively thick MNG, due to the enabling effect of faults cutting the GHSZ far from the top of the GHSZ; (3) the undisturbed state of the FGZ outside the extent of the MNG; and (4) the disequilibrium state of the base of the GHSZ due to the unloading of sediments in an unstable slope environment prone to failure.