The assumption that the magnetic entropy is stationary (SME) in the tokamak consistently with the Grad-Shafranov-Schlüter equation (GSS) restricts the toroidal current density and pressure profiles to special forms characterised by few global parameters. The procedure provides a method for analysing and classifying the data from the point of view of general principles, independent of the details of the underlying dynamics. This method of analysis has been applied to the plasma profiles on different tokamaks (JET, FTU) so as to verify its reliability under different conditions of geometry and auxiliary heating. This paper is focused on the implications on energy transport in both L (Ip = 1.6MA, Bt = 3.2T, 2-9MW NBI + 3.7MW ICRH in mode conversion scheme) and H (Ip = 2.8MA, Bt = 2.8T, 14MW of ICRH+NBI) mode JET plasmas in which electron and ion heating have been carefully tailored in order to investigate the electron stiffness.