In this paper, we consider the effect of external force on the large-time behavior of solutions to the Cauchy problem for the three-dimensional full compressible Navier–Stokes equations. We construct the global unique solution near the stationary profile to the system for the small H2(R3) initial data. Moreover, the optimal Lp–L2 time decay rates of the solution to the system are established via a low frequency and high frequency decomposition.