We further develop a thermal LB model for multiphase flows. In the improved model, we propose to use the windowed FFT and its inverse to calculate both the convection term and external force term. By using the new scheme, Gibbs oscillations can be damped effectively in unsmooth regions while the high resolution feature of the spectral method can be retained in smooth regions. As a result, spatiotemporal discretization errors are decreased dramatically and the conservation of total energy is much better preserved. A direct consequence of the improvements is that the unphysical spurious velocities at the interfacial regions can be damped to neglectable scale. With the new model, the phase diagram of the liquid-vapor system obtained from simulation is more consistent with that from theoretical calculation.Very sharp interfaces can be achieved. The accuracy of simulation results is also verified by the Laplace law. The high resolution, together with the low complexity of the FFT, endows the proposed method with considerable potential, for studying a wide class of problems in the field of multiphase flows and for solving other partial differential equations.