The response of the electron temperature profiles to changes in heating profile is investigated analytically and by transport code simulations. A heat conduction model with local empirical scalings of the electron thermal diffusivity χe is used. It is found that the Te-profile responds rather insensitively, owing to double radial integration of the heating power density. By scanning the target density and injection energy of neutral beam heated ASDEX plasmas it is shown that only small profile changes in the conductive electron heat flux are achieved. In density scans these changes are further diminished by the convective power loss. The theoretically predicted variation in Te(r)/Te(0) is correspondingly weak and does not exceed the measured profile change. The observed Te profile invariance is thus produced by local transport models with a diffusive electron heat flux proportional to dTe/dr. Consequently, it is not necessary to introduce a χe(r) which adjusts to the profile of the conductive electron heat flux or which non-linearly depends on the electron temperature gradient.