  The steady states of two gases of hard spheres or disks separated by an
adiabatic piston in presence of a temperature gradient are discussed. The
temperature field is generated by two thermal walls at different temperatures,
each of them in contact with one of the gases. The presence of the piston
strongly affects the hydrodynamic fields, inducing a jump in its vicinity. A
simple kinetic theory model is formulated. Its predictions are shown to be in
good agreement with molecular dynamics simulation results. The applicability of
the minimum entropy production principle is analyzed, and it is found that it
only provides an accurate description of the system in the limit of a small
temperature gradient.
