We study finite-temperature phase transitions in a two-dimensional boson Hubbard model with zero-point quantum fluctuations via Monte Carlo simulations of a quantum rotor model and construct the corresponding phase diagram. Compressibility shows a thermally activated gapped behavior in the insulating regime. Finite-size scaling of the superfluid stiffness clearly shows the nature of the Kosterlitz-Thouless transition. The transition temperature T(c) confirms a scaling relation T(c) proportional, rho(0)(x), with x=1.0. Some evidence of anomalous quantum behavior at low temperatures is presented.