The seafloor topography and heat flux differ significantly from the predictions of the half-space cooling (HSC) model at old ocean basins. Understanding the deviations has important implications for thermal evolution of oceanic lithosphere and large-scale mantle dynamics. A widely used model that explains significant fraction of the deviations is the plate model, but the dynamical feasibility of the plate model has never been demonstrated. In this study, we investigated the effects of sublithospheric small-scale convection (SSC) and of internal heating on seafloor heat flux and topography and mantle thermal structure, and we examined the dynamic feasibility of the plate model by formulating high- resolution two-dimensional numerical models of mantle convection with strongly temperature- and depth-dependent rheology. We found that mantle convection with tectonic plates often leads to formation of a broad thermal anomaly below old lithosphere where the mantle is not cooled by subducted slabs and heat transfer is less efficient because of thick lithosphere, especially when significant internal heating is present. This trapped heat may exist in the middle mantle when the SSC is absent, and it may also be redistributed by the SSC to shallow depths to reheat the lithosphere and to homogenize mantle temperature. When internal heating accounts for >~60% of the total heat output, the trapped heat may provide sufficient heat supply to preferentially reheat old lithosphere via SSC while maintaining uniform mantle temperature. We suggest that the trapped heat and the SSC are responsible for the residual heat flux and topography at old ocean basins relative to the HSC model predictions. Our models also show that for the plate model to be dynamically viable, both the SSC and significant internal heating (>60%) are necessary. This is because only the SSC in a mantle with significant internal heating can erode and reheat the lithosphere while maintaining a nearly constant mantle temperature below lithosphere, which is the basic assumption of the plate model. With the viscosity structure and internal heating rate for the present-day mantle, we think that the plate model is dynamically viable.