The anomalously fast relaxation of the perturbations to the electron temperature profile caused by a sawtooth crash has been studied extensively on TFTR. It is shown that on a short time-scale the heat pulse is not simply diffusive as has been generally assumed, but that modelling of the heat pulse requires a transient enhancement in χe following the sawtooth crash. It is also shown that the time dependent enhancement in χe predicted by non-linear thermal transport models, i.e. incremental chi models or the Rebut-Lallia-Watkins transport model, is much smaller than that required to explain the anomalies in the heat pulse propagation