The dielectric properties of the hydrogen disordered hexagonal phase (Ih) of water ice have been computed using density functional theory (DFT) based Monte Carlo simulations in the isobaric-isothermal ensemble. Temperature dependent data yield a fit for the Curie-Weiss law of the system and hence a prediction of the temperature of the phase transition from the Ih phase to the hydrogen ordered ice XI phase. Direct simulations around the phase transition temperature confirm and refine the predicted phase transition temperatures and provide data for further properties, such as the linear thermal expansion coefficient. Results have been obtained with both hybrid and semilocal density functionals, which yields insight in the performance of the electronic structure method. In particular, the hybrid functional yields significantly more realistic dielectric constants than the semilocal variant, namely ε ≈ 116 as opposed to ε ≈ 151 at 273 K (εexperiment = 95). This can be attributed to the tendency of semilocal functionals to be biased to configurations with a large dipole moment, and their overestimation of the dipole moments of these configurations. This is also reflected in the estimates of the Ih/XI transition temperature, which is 70-80 and 90-100 K for the hybrid and semilocal functional respectively. DFT based sampling of the millions of configurations necessary for this work has been enabled by a Tree Monte Carlo algorithm, designed for massively parallel computers.