  We discuss the stochastic mean-field theory (SMFT) method which is a new
approach for describing disordered Bose systems in the thermodynamic limit
including localization and dimensional effects. We explicate the method in
detail and apply it to the disordered Bose-Hubbard model at finite temperature,
with on-site box disorder, as well as experimentally relevant unbounded speckle
disorder. We find that disorder-induced condensation and reentrant behavior at
constant filling are only possible at low temperatures, beyond the reach of
current experiments [Pasienski et al., arXiv:0908.1182]. Including off-diagonal
hopping disorder as well, we investigate its effect on the phase diagram in
addition to pure on-site disorder. To make contact to present experiments on a
quantitative level, we also combine SMFT with an LDA approach and obtain the
condensate fraction in the presence of an external trapping potential.
