Elucidating the radiative-dynamical coupling between the upper photosphere and deeper atmosphere may be key to our understanding of the abnormally large radii of hot Jupiters. Very long integration times of 3D general circulation models (GCMs) with self-consistent radiative transfer are needed to obtain a more comprehensive picture of the feedback processes between dynamics and radiation. Here, we present the longest 3D nongray GCM study to date (86 000 d) of an ultra-hot Jupiter (WASP-76 b) that has reached a final converged state. Furthermore, we present a method that can be used to accelerate the path toward temperature convergence in the deep atmospheric layers. We find that the final converged temperature profile is cold in the deep atmospheric layers, lacking any sign of vertical transport of potential temperature by large-scale atmospheric motions. We therefore conclude that coupling between radiation and dynamics alone is not sufficient to explain the abnormally large radii of inflated hot gas giants.