The hot-tail electron distribution evolution after the Shattered Pellet Injection could be of significant interest to the disruption mitigation community due to two aspects: first, the hot-tail electrons serve as strong runaway electron seed in a rapidly cooling plasma and contribute to the "jump-start" of the runaway electron current generation; second, the hot-tail electrons would result in additional ablation of the pellet fragments thus result in more edge-localized injection deposition as well as shallower fragment penetration in case of total ablation of fragments. To take a deeper look at these two issues, we hereby investigate the hot-tail thermalization dynamics and their overall impact to the injection penetration. 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. The solid fragments thus serve as a sink for the hot-tail runaway seed electrons and is beneficial to the runaway current mitigation in the Current Quench phase. Additionally, 2D JOREK simulation incorporating the above hot-tail electron contribution 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.