The temperature and pressure dependence of the previously developed polarizable atomic-multipole-based AMOEBA water potential is explored. The energetic, structural, and dynamical properties of liquid water are investigated via molecular dynamics simulations at various temperatures ranging from 248 K to 360 K and pressures up to 5000 atm. The AMOEBA model, derived solely from known gas-phase and room-temperature liquid properties, produces a maximum liquid density around 290 K at I atm. The quantitative agreement between AMOEBA and experiment is good in general for density, heat of vaporization, radial distribution functions, magnetic shielding, self-diffusion, and static dielectric constant. Based on comparison of two variants of AMOEBA water, as well as results from other water potentials, it is suggested that the temperature at which the maximum density occurs is closely related to the tetrahedral hydrogen-bonding network in the bulk. Explicit dipole polarization and internal geometry in the liquid play vital roles in determining the self-diffusion and dielectric constants. The development of the AMOEBA model demonstrates that a realistic and well-balanced atomic potential requires a sophisticated electrostatic description and inclusion of many-body polarization. Within the current polarizable atomic multipole framework, a potential derived from limited gas phase and condensed phase properties can be applied across a range of physical and thermodynamic environments.