Standard analysis treats the sawtooth induced heat pulse as a diffusive phenomenon by linearising the diffusion equation around the unperturbed state of the plasma. This implies that the heat pulse is governed by the incremental thermal diffusivity. This approach has been criticized by Fredrickson, who claim that turbulence associated with the sawtooth collapse affects the propagation of the heat pulse. It is shown that due to a fundamental misconception their modelling with a time-dependent diffusivity (the 'ballistic' heat pulse) is incorrect and leads to invalid conclusions. We demonstrate that the measurements impose a temporary change of the effective thermal diffusivity during the heat pulse which is similar to the implicit time behaviour imposed by the linearised treatment.