We study the finite temperature quantum rotor model with capacitive disorder. Such a model may serve as an idealized Hamiltonian for Josephson junction arrays. By using a mean-field approximation, we compute the average free energy and the equation for the phase boundary line between the insulating and superconducting phases. We find that the Mott-insulating lobe structure disappears for large variance sigma ~ 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 $\sigma$. 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.