[en] The redistribution of the current density in a high temperature plasma is usually described in terms of the magnetic field diffusion associated with the collisional resistivity relevant to the specific physical and geometrical properties of the plasma. Yet there are indications that it should not be sufficient to relate the applied electric field E_parallel to J_parallel through the collisional resistivity η only, in order that the appropriate current density profiles be reproduced. In regimes where a significant fraction of the electron population is trapped and the collisional resistivity is given by the so-called neoclassical expression, the resulting current density profile is strange if the electron temperature radial profile is close to a Gaussian. The authors assume that in ohmic regimes, where the applied electric field drives the current and at the same time heats the plasma, the transport of the electron thermal energy and the redistribution of the current density are strongly coupled. They consider a matrix equation that describes the transport for both quantities under steady state conditions, they postulated symmetry properties of the elements of this matrix and use them to define two transport coefficients: an effective thermal conductivity and a thermal-viscous coefficient. An integro-differential equation is derived from the matrix transport equation and the resulting steady state electron temperature and current density profiles, as obtained from numerical solutions, are presented. They propose that the degradation that occurs in the presence of injected heating is associated with the decoupling between the thermal energy transport and the current energy transport when the electric field is no longer the source for both. In this case, they argue that the contribution to the electron thermal energy diffusion coefficient by collective modes that do not depend directly on the current density distribution becomes prevalent. 2 refs