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.Comment: 6 pages, Revtex, 6 figures (available on request from the authors
