We are concerned with the large-time behavior of solutions to the initial and initial boundary value problems with large initial data for the compressible Navier-Stokes system with degenerate heat-conductivity describing the one-dimensional motion of a viscous heat-conducting perfect polytropic gas in unbounded domains. Both the specific volume and temperature are proved to be bounded from below and above independently of both time and space. Moreover, it is shown that the global solution is asymptotically stable as time tends to infinity.