  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 Mott-insulating lobe structure disappears for large
variance ($\sigma \gtrsim e$) 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.
