Ice 1h is studied by molecular-dynamics simulations using the SPC/E model of water. The simulations were carried out in the constant stress, constant temperature ensemble, over a range of temperature and external pressure. By heating the system at 10 K intervals every 100 ps, we establish an upper bound for the stability of the ice 1h structure at 1 atmosphere to be below 260 K for the SPC/E model. The shape of the crystal lattice does not change significantly from the ideal hexagonal structure of ice 1h, even close to the melting transition. This is significant for future investigations of the ice-water interface using molecular simulations.