  In this paper, we consider the heat-conducting compressible self-gravitating
fluids in time-dependent domains, which typically describe the motion of
viscous gaseous stars. The flow is governed by the 3-D
Navier-Stokes-Fourier-Poisson equations where the velocity is supposed to
fulfil the full-slip boundary condition and the temperature on the boundary is
given by a non-homogeneous Dirichlet condition. We establish the global-in-time
weak solution to the system. Our approach is based on the penalization of the
boundary behavior, viscosity, and the pressure in the weak formulation.
Moreover, to accommodate the non-homogeneous boundary heat flux, the concept of
{\em ballistic energy} is utilized in this work.
