We present recent observations of the plasma parameters in coronal holes at
the origin of the fast solar wind and in the interplanetary medium. A mode
l based on the heat conductivity law in a dilute plasma shows the coherency
of the electron and proton temperature observations from coronal holes to
the interplanetary medium. These new observations are severe constraints fo
r any model of the expansion of the fast solar wind. We discuss why and how
non-equilibrium multispecies Fokker-Planck approach must be developed and
present a generalized Grad's solution.