Fits to the 1D equilibrium temperature-pressure (T_eq – left) and Newtonian cooling relaxation timescale (τ_rad – right) profiles, which form the basis of the profiles used in our models of Kepler-13Ab (top), KELT-1b (middle), and SDSS1411B (bottom). In all cases, the equilibrium 1D profile is shown in light grey, and the linear in space fit is shown in orange. Note that depending upon the model parameters, including the pressure at which day-night temperaturedifferences go to zero and presence of deep radiative dynamics, these fits may be truncated or modified as required. For full details of the exact fit used in each model, see both Tables 3 and 4.