Classical molecular dynamics simulations of water adsorbed in silicalite, a hydrophobic all-silica zeolite, were performed at different temperatures in the range 100-580 K, to explore possible phase transitions and to compare the behavior of adsorbed water with that of bulk water or water confined in nanopores of different geometry. We used a potential model including full flexibility both of water molecules and of the silicate framework. The results show an unexpected complexity. At very low temperatures (below 225 K), water appears to be mostly in form of amorphous solidlike clusters among which a slow molecule interchange occurs, giving rise to a single-file like diffusion on the time scale of our simulations. At intermediate temperatures, in the approximate range of 225-350 K, the behavior of water is almost liquidlike, whereas at higher temperatures, there are evidences of a vaporlike features, in agreement with the suggestions of previous theoretical and experimental works. This behavior is discussed by considering, among others, the average distribution of water in the channels, the size and lifetime of the hydrogen bonded clusters, and the water-water interaction energy. The results are compared with the available experimental data, previous simulations, and statistical mechanical studies.