The authors study a simple model of a nematic liquid crystal made of parallel ellipsoidal particles interacting via a repulsive Gaussian law. After identifying the relevant solid phases of the system through a careful zero-temperature scrutiny of as many as eleven candidate crystal structures, they determine the melting temperature for various pressure values, also with the help of exact free energy calculations. Among the prominent features of this model are pressure-driven reentrant melting and the stabilization of a columnar phase for intermediate temperatures.