The origin of the reduced electron heat diffusivity chi-e and the diffusion coefficient D in the core of H-mode plasmas is explored. By statistical analyses of 38 H-mode discharges in ASDEX it is shown that in the L- and H-regimes the electron temperature profile shape is invariant in the outer half of the plasma. On the basis of this profile invariance and the edge temperatures in the L- and H-phases the magnitude, the weak radial dependence and the short time-scale of the reduction of chi-e in the bulk plasma are explained. The constancy of the T(e) profile shape yields a nonlocal contribution to the anomalous transport and accounts for the regime dependent factors in the empirical scalings of chi-e and D used up to now. It is further shown that T(e) profile invariance can explain the power dependence of chi-e and of the energy confinement time in the intermediate regime between Ohmic heating (OH) and pure L-mode confinement and the delayed L-OH transition after neutral beam injection.