The time evolution of neutron emission has been measured in sawtoothing discharges in the Frascati Tokamak (FT). The observed change in the neutron emission level during the sawtooth crash has been studied in terms of variations of the deuteron density and temperature. Changes of the peak values of these quantities as well as profile changes have been considered. It is shown that the occurrence of a net ion energy outflow through the mixing radius after a sawtooth collapse can explain the observed drop in the neutron emission. The model is also used to infer the ion thermal conductivity near the plasma centre which is found to be compatible with neoclassical predictions.