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Bosons in a periodic lattice with on-site disorder at low but non-zerotemperature are considered within a mean-field theory. The criteria used forthe definition of the superfluid, Mott insulator and Bose glass are analysed.Since the compressibility does never vanish at non-zero temperature, it can notbe used as a general criterium. We show that the phases are unambiguouslydistinguished by the superfluid density and the density of states of thelow-energy exitations. The phase diagram of the system is calculated. It isshown that even a tiny temperature leads to a significant shift of the boundarybetween the Bose glass and superfluid

Mean-field phase diagram of disordered bosons in a lattice at nonzero temperature