The anomously fast relaxation of the perturbations to the electron tem
perature profile caused by a sawtooth crash has been studied extensive
ly on TFTR. It is shown that on a short time-scale the heat pulse is n
ot simply diffusive as has been generally assumed, but that modelling
of the heat pulse requires a transient enhancement in chi(e) following
the sawtooth crash. It is also shown that the time dependent enhancem
ent in chi(e) predicted by non-linear thermal transport models, i.e. i
ncremental chi models Dr the Rebut-Lallia-Watkins transport model, is
much smaller than that required to explain the anomalies the heat puls
e propagation.