  We consider the Navier--Stokes--Fourier system describing the motion of a
compressible, viscous, and heat conducting fluid in a bounded domain with
general non-homogeneous Dirichlet boundary conditions for the velocity and the
absolute temperature, with the associated boundary conditions for the density
on the inflow part. We introduce a new concept of weak solution based on the
satisfaction of the entropy inequality together with a balance law for the
ballistic energy. We show the weak-strong uniqueness principle as well as the
existence of global-in-time solutions.
