Observations up to the present indicate that the climatological volume transports of the Kuroshio have an annual range of at most 10 Sv and a maximum in summer, both of which are inconsistent with the nontopographic Sverdrup relation. We show that these observed properties may be reproduced using a two-layer planetary geostrophic model with variable bottom topography if we take into account sea-surface heat flux, as well as large interface displacements associated with layer outcropping. The thermal forcing is represented by seasonally changing the reduced gravity so that the available potential energy of the model ocean is decreased in winter and increased in summer, consistent with the seasonal air-sea heat exchange. From numerical experiments we find that the bottom topography accelerates conversion between available potential energy and kinetic energy of the barotropic flow so as to compensate for the change in the energy storage due to the heat transfer. In particular, winter cooling intensifies conversion from barotropic kinetic energy to available potential energy, leading to a further decrease in the winter transport, and the reverse takes place in summer, so that the summer transport may exceeds the winter transport.