  We consider the Navier-Stokes-Fourier system on an unbounded domain in the
Euclidean space $R^3$, supplemented by the far field conditions for the phase
variables, specifically: $\rho \to 0,\ \vartheta \to \vartheta_\infty, \ u \to
0$ as $\ |x| \to \infty$. We study the long time behaviour of solutions and we
prove that any global-in-time weak solution to the NSF system approaches the
equilibrium $\rho_s = 0,\ \vartheta_s = \vartheta_\infty,\ u_s = 0$ in the
sense of ergodic averages for time tending to infinity. As a consequence of the
convergence result combined with the total mass conservation, we can show that
the total momentum of global-in-time weak solutions is never globally
conserved.
