In this work, we simulated MP2 water using an NNP at different temperatures using classical and quantum dynamics. MP2 theory, though belonging to the fifth rung of the electronic structure "Jacob's ladder", is unable to predict accurately the static and dynamical properties of liquid water. This may be because an insufficiently large basis set causes MP2 theory to overestimate the Van der Waals interaction. This may be improved upon by increasing the basis set to quadruple-ζ and larger, or by estimating the difference between the results of small and large basis sets using cluster models and decomposing the error into two-and three-body interaction terms, which can be used to further cancel the basis-set error. Alternatively, double-hybrid density functionals based on MP2 and random-phase approximation may be used to train the NNP: they exhibit faster convergence with basis set size at similar computational cost as the parent correlated methods . Although nuclear quantum effects reduce the height of the first peak of the oxygen-oxygen radial distribution function at room temperature, the match with the experimental RDF is still not perfect. However, a better agreement with experimental RDFs is observed at an elevated temperature of 340 K, at which MP2 predicts stratifying static properties of liquid water compared to the experimental data, as characterized by the RDFs, triplet angles distribution, and tetrahedral local order parameters. It is possible that the elevated temperature cancels the error due to an insufficient basis set, higher kinetic energy compensating for the overestimation of dispersion by MP2 theory.