  We study stationary states of a one-dimensional gas of granular point-like
particles not subject to gravity between two walls at temperatures T- and T+,
with T- < T+. Depending on the normalized temperature difference Delta = (T+ -
T-)/(T+ + T-) the system may be completely fluidized, or in a mixed state in
which a cluster coexists with the fluidized gas. We devise and explain in
detail a method for integrating the one-dimensional dissipative Boltzmann
equation in the test-particle limit for the stationary case. We then apply this
method to test the equation's validity up to the clustering regime, by
comparing with results from microscopic Newtonian molecular dynamics. There is
very good agreement, with the one-particle phase space density function
presenting highly non-Gaussian features, and a discontinuity that corresponds
to the test-particle limit. We conclude that Boltzmann's equation is valid at
least everywhere in the control parameter space where the system has no
cluster. The behavior of the system in its fluid phase is dominated by
characteristic lines which resemble trajectories of particles subjected to a
force which attracts them to a fixed point. If this point is in the physical
region a cluster forms, if not then the system remains fluid.
