Coulomb repulsion is taken into account to derive the thermodynamics of charged bosons in a random external potential. A simple analytical form of the partition function is proposed for the case of non-overlapping localised states (i.e. a small amount of disorder). The density of localised bosons and the specific heat show a peculiar non-uniform temperature dependence below the Bose-Einstein condensation temperature. The superfluid - Bose-glass phase diagram is discussed. A new phase is predicted which is a Bose-glass at T=0 but a superfluid at finite T.
This is a pre-print. It is also available at: http://arxiv.org/abs/cond-mat/9704164.