The anomalously large radii of highly irradiated exoplanets have long remained a mystery to the Exoplanetary community, with many different solutions suggested and tested. These solutions have included tidal heating of the atmosphere, or ohmic heating from a strong magnetic field. Another solution was also suggested by Tremblin et Al. (2017): The inflated radii of highly irradiated exoplanets can be explained by the advection of potential temperature, via mass and longitudinal momentum conservation, leads to the deep atmosphere attaching to a hotter adiabat than would be suggested by 1D models, thus implying an inflated radius. In that paper this mechanism was tested using 2D steady-state models, and successfully reproduced an inflated HD209458b scenario. Here we extend this work to both the time-dependent and 3D regimes using the GCM Dynamico (Itself developed as a new dynamical core for LMD-Z, and verified against Hot Jupiter benchmarks as part of this work), exploring the evolution of the deep P-T profile, and the stability of a deep adiabat as the steady state solution. As a result of these calculations we confirm that a deep, hot, adiabat is both the target of long term evolution of the deep atmosphere, and is stable against typical forcing expected at deep pressures — we also note that this deep adiabat takes a very significant time to form from an isothermal initial condition (hence why it has not previously been seen in GCM simulations beyond a kink in the deep profile), and suggest that future GCM models should use an adiabatic profile to initialise the deep atmosphere. Taken as a whole, our results confirm the theory of Tremblin et Al. (2017): the inflated radii of highly irradiated exoplanets can be explained by connecting the atmosphere with a deep, hot, internal adiabat.