  Using one-dimensional hybrid expanding box model we investigate properties of
the solar wind in the outer heliosphere. We assume a proton-electron plasma
with a strictly transverse ambient magnetic field and, beside the expansion, we
take into account influence of a continuous injection of cold pick-up protons
through the charge-exchange process between the solar wind protons and hydrogen
of interstellar origin. The injected cold pick-up protons form a ring
distribution function that rapidly becomes unstable and generate Alfv\'en
cyclotron waves. The Alfv\'en cyclotron waves scatter pick-up protons to a
spherical shell distribution function that thickens over that time owing to the
expansion-driven cooling. The Alf\'ven cyclotron waves heat solar wind protons
in the perpendicular direction (with respect to the ambient magnetic field)
through the cyclotron resonance. At later times, the Alfv\'en cyclotron waves
become parametrically unstable and the generated ion acoustic waves heat
protons in the parallel direction through the Landau resonance. The resulting
heating of the solar wind protons is efficient on the expansion time scale.
