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The fragment ablation rate plays significant roles in the mitigation efficiency of Shattered Pellet Injection (SPI) as a Disruption Mitigation System (DMS). Current mainstream 3D MHD codes modelling SPIs mostly assume instantaneous thermalization between the previously hot ambient electrons and the newly released cold electrons, which results in underestimation of the ablation rate if the hot electron thermalization time is comparable or even longer than the fragment flying time. To resolve this doubt, we hereby investigate the thermalization dynamics and the overall hot-electron impact. The finite-time collisional thermalization of hot-tail electrons in a rapidly cooling plasma, as well as the so-called ``self-limiting'' effect are considered. The former effect tends to deplete the colder population within a hot-tail species, while the latter is found to preferentially deplete the higher energy population. The combined result is found to cause an almost self-similar decay of the hot electron distribution function, while its shape does not deviate much from that of Maxwellian distribution and the mean energy does not change much during the thermalization process. Based on this observation, axisymmetric JOREK D2 SPI simulations were carried out with additional hot-tail contribution to evaluate their overall impact onto the injection assimilation and penetration. It is found that the hot-tail effect indeed causes enhanced assimilation and shallower penetration, although the overall effect depends on the exact injection configuration, with the slow injection showing negligible hot-tail effect while the fast single non-shattered pellet case shows drastic hot-tail ablation enhancement. For ITER-like SPI parameters, there is no significant deviation in the total assimilation, but some deviation in the injection penetration is observed for the fast injection velocity cases.