  The heat conducting compressible viscous flows are governed by the
Navier-Stokes-Fourier (NSF) system. In this paper, we study the NSF system
accomplished by the Newton law of cooling for the heat transfer at the
boundary. On one part of the boundary, we consider the Navier slip boundary
condition, while in the remaining part the inlet and outlet occur. The
existence of a weak solution is proved via a new fixed point argument. With
this new approach, the weak solvability is possible in Lipschitz domains, by
making recourse to \(L^q\)-Neumann problems with \(q>n\).Thus, standard
existence results can be applied to auxiliary problems and the claim follows by
compactness techniques. Quantitative estimates are established.
