  A simplified, but non trivial, mechanical model -- gas of $N$ particles of
mass $m$ in a box partitioned by $n$ mobile adiabatic walls of mass $M$ --
interacting with two thermal baths at different temperatures, is discussed in
the framework of kinetic theory. Following an approach due to Smoluchowski,
from an analysis of the collisions particles/walls, we derive the values of the
main thermodynamic quantities for the stationary non-equilibrium states. The
results are compared with extensive numerical simulations; in the limit of
large $n$, $mN/M\gg 1$ and $m/M \ll 1$, we find a good approximation of
Fourier's law.
