Radial profile of the temperature difference and of the sub-adiabaticity of a 1D solar-like structure with a modified temperature gradient in the overshooting layer according to Eqs. (2)–(5). The temperature gradient is modified over a distance d_ov = α_ovH_P, CB, with α_ov = 0.15 in the lower panel and α_ov = 0.20 in the upper panel. The dash-dotted red lines show the percentage relative temperature difference, ΔT/T_ref, with ΔT = T − T_ref. The solid blue lines correspond to the sub-adiabaticity (∇−∇_ad). The dashed black lines show the sub-adiabaticity of the reference model. The convective boundary is indicated by the vertical solid line. The vertical dashed line in each panel is located at a distance d_ov below the convective boundary.