The dielectric constant of a polarizable water model is estimated for several thermodynamic states at elevated temperatures and reduced densities relative to ambient conditions using molecular dynamics simulations. An extended Lagrangian formulation of induced polarization is used in these simulations in conjunction with thermostat variables. This approach to the simulation of induced polarization is found to require about one-half the computational effort needed to determine directly the adiabatic values for the induced dipole moments. As the temperature increases and the density decreases, the difference between the model and experimental values of the dielectric constant is positive and significantly larger than the uncertainty in the model values.