The response of the electron temperature profile shape to variations of the electron heating and density profiles is investigated in different confinement regimes. It is shown that the changes in r(Te) = -T(e)/(dT(e)/dr) exceed the measurement error if the shape of the electron heat diffusivity chi(e)(r) is kept fixed. The observed constancy of r(Te)(r) in the outer half of the plasma is incompatible with such a fixed chi(e)(r) shape, i.e. a T(e) profile constraining mechanism must be present. Local transport laws of the form chi(e) is-proportional-to r(Te)-alpha with alpha greater than or similar to 4 and chi(e) is-proportional-to (dT(e)/dr)alpha with alpha greater-than-or-equal-to 2 yield the experimental stiffness of the T(e)(r) shape but conflict with empirical chi(e) scalings. These results support the model of a self-organizing and adjusting chi(e)(r) causing T(e) profile invariance.