Absolutely pure water is neutral, although even trace amounts of impurities could affect these ion concentrations and the water may no longer be neutral. Kw is sensitive to both pressure and temperature; it increases when either increases.
As temperature increases, pKwdecreases; and as temperature decreases, pKw increases (for temperatures up to about 250 °C). This means that ionization of water typically increases with temperature.
There is also a (usually small) dependence on pressure (ionization increases with increasing pressure). The dependence of the water ionization on temperature and pressure has been well investigated and a standard formulation exists.