  We study convergence of a finite volume scheme for the Navier-Stokes-Fourier
system describing the motion of compressible viscous and heat conducting
fluids. The numerical flux uses upwinding with an additional numerical
diffusion of order $\mathcal{O} (h^{ \varepsilon+1})$, $0<\varepsilon<1$. The
approximate solutions are piecewise constant functions with respect to the
underlying mesh. We show that any uniformly bounded sequence of numerical
solutions converges unconditionally to the solution of the
Navier-Stokes-Fourier system. In particular, the existence of the solution to
the Navier-Stokes-Fourier system is not a priori assumed.
