Electron heat transport on TFTR and other tokamaks is several orders of magnitude larger than neoclassical calculations predict. Despite considerable effort, there is still no clear theoretical understanding of this anomalous transport. The electron temperature profile, Te(r), has shown a marked consistency on many machines for a wide range of plasma parameters and heating profiles. This could be an important clue as to the process responsible for this enhanced thermal transport. In the first section of the paper the result is presented that TFTR electron temperature profile shapes are even more constrained than previous models of profile consistency suggested. The profile shapes, Te(r)/Te(a/2), are found to be invariant (for r > 0.4 a) for a wide range of parameters, including q(a). In the second section, an experiment is discussed which uses a fast current ramp to transiently decouple the current density profile, J(r), and the Te(r) profiles. From this experiment, it has been determined that the J(r) profile can be strongly modified with no measurable effect on the electron temperature profile shape. Thus, while the electron temperature profile is apparently constrained, the current profile is not.