  This paper is devoted to the global existence of weak solutions to the
three-dimensional compressible Navier-Stokes equations with heat-conducting
effects in a bounded domain. The viscosity and the heat conductivity
coefficients are assumed to be functions of the temperature, and the shear
viscosity coefficient may vanish as the temperature goes to zero. The proof is
to apply Galerkin method to a suitable approximate system with several
parameters and obtain uniform estimates for the approximate solutions. The key
ingredient in obtaining the required estimates is to apply De Giorgi's
iteration to the modified temperature equation, from which we can get a lower
bound for the temperature not depending on the artificial viscosity coefficient
introduced in the modified momentum equation, which makes the compactness
argument available as the artificial viscous term vanishes.
