Disruptions pose a serious challenge for future tokamak power plants; at the large stored thermal and magnetic energies of ITER and DEMO plasmas, the heat loads and electromagnetic forces during disruptions must be mitigated. With this objective, JET experiments employing impurity shattered pellet injection (SPI) have recently been undertaken. We present numerical models of SPI disruptions in JET using M3D-C1, an extended-MHD code developed for the study of non-linear transient events in tokamaks. Among its extensions are a neutral gas shielding model for the ablation of frozen pellets within the plasma, and the non-coronal equilibrium model KPRAD for tracking impurity charge states and radiation. With these, plasma cooling both before the thermal quench (when there is little MHD activity) and during it (when instability provokes rapid cooling of the plasma core) can be modelled. Our results concern the cooling of ohmic JET plasma #95149 by a small shattered Neon-Deuterium pellet, modelled in M3D-C1 both with linearised stability analyses of axisymmetric simulations, and with a fully non-linear three-dimensional model. Comparisons are made with experimental measurements of temperature profiles and radiated power during the pre-thermal quench phase, and the timing and nature of thermal quench onset as the pellet impinges on rational surfaces and excites low-n MHD activity. This analysis qualifies the numerical approach, paving the way to simulations of higher-energy JET discharges and predictions for future devices.