In this chapter, we prove the existence of a variational solution to the system of equations describing flow of the compressible viscous heat conducting fluid in time dependent domain supplemented with slip boundary conditions for velocity and conservative boundary condition for the heat flux. Similarly as in Chap. 4 , the main ingredient of the proof is the penalization of the boundary condition. Moreover, several other approximation parameters need to be introduced and successive limit procedures are made to prove the main theorem. The problem of existence of solutions to the approximated system presents an interesting problem itself and is also addressed. Finally, necessary adjustments needed to prove the theorem for Dirichlet boundary condition for the velocity field are discussed.