We study the phase diagram at finite temperature of Josephson junction arrays with capacitive disorder (i.e., random offset charges and/or random charging energies): in the limit of large particle numbers per junction, this is a remarkable physical realization of the disordered boson Hubbard model. By using a mean-field approximation, we compute the average free energy and the equation for the phase boundary line between the insulating and the superconducting phase. We find that the

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... ing lobe structure disappears for large variance (σ≳ e) of the offset charges probability distribution. Further, with nearest-neighbor interactions, the insulating lobe around q=e is destroyed even for small values of σ. In the case of random charging energies, until the variance of the distribution reaches some critical value the superconducting phase increases in comparison to the situation in which all self-capacitances are equal.