We present a kinetic collisionless model of the solar wind generalized to take into account the spiral structure of the interplanetary magnetic field. This model, which also includes Kappa velocity distributions, calculates self-consistently the electric potential profile and derives the solar wind speed and the temperatures of the medium. We study how the inclusion of the spiral geometry changes the plasma parameters compared to the case of a radial magnetic field. Whereas the interplanetary electric potential, the wind density and bulk speed are not significantly changed, we show that the electron and proton temperatures are modified; in particular, we find a decrease of the proton temperature and of its anisotropy, and an increase of the electron temperature. We discuss these results and the validity of the model.