In this talk, we will consider the following two issues for the Cauchy problem to the heat conductive compressible Navier-Stokes equations in the presence of far field vacuum: (i) regularities of solutions in the inhomogeneous Sobolev spaces; (ii) uniform boundedness of the entropy. The previous works concerning these two issues focus on the case in one dimension. While in this talk, we will update the results for the case in multi-dimensions. This talk is based on a recent joint work with Prof . Zhouping Xin.