Various steady state non-inductive plasmas, with strong electron heating and significant modification of the current density profile, have been routinely obtained in Tore Supra discharges with lower hybrid current drive (LHCD) and/or fast wave electron heating (FWEH) experiments. The dependence of the electron heat diffusivity χe on the electron temperature gradient ∇Te, the magnetic shear s and the safety factor q is demonstrated. The increase of χe with ∇Te indicates the existence of a critical temperature gradient. Moreover, the current density profile affects the global confinement and the local transport. The electron heat flux qe is found to be roughly proportional to q2. The effect of magnetic shear on χe is studied in the improved confinement discharges obtained by modifying the current profile. When the magnetic shear increases in the confinement zone and/or vanishes in the plasma centre, χe decreases. The effect of the current profile is also observed in the saturated ohmic regime. The results for χe do not agree with the local transport models of Taroni et al. or Rebut-Lallia-Watkins (RLW) for all ranges of electronheating.