  We study the convergence and error estimates of a finite volume method for
the compressible Navier-Stokes-Fourier system with Dirichlet boundary
conditions. Physical fluid domain is typically smooth and needs to be
approximated by a polygonal computational domain. This leads to domain-related
discretization errors, the so-called variational crimes. To treat them
efficiently we embed the fluid domain into a large enough cubed domain, and
propose a finite volume scheme for the corresponding domain-penalized problem.
Under the assumption that the numerical density and temperature are uniformly
bounded, we derive the ballistic energy inequality, yielding a priori estimates
and the consistency of the penalization finite volume approximations. Further,
we show that the numerical solutions converge weakly to a generalized, the
so-called dissipative measure-valued, solution of the corresponding Dirichlet
problem. If a strong solution exists, we prove that our numerical
approximations converge strongly with the rate 1/4. Additionally, assuming
uniform boundedness of the approximate velocities, we obtain global existence
of the strong solution. In this case we prove that the numerical solutions
converge strongly to the strong solution with the optimal rate 1/2.
