  In the framework of the trap-size scaling theory, we study the scaling
properties of the Bose-Hubbard model in two dimensions in the presence of a
trapping potential at finite temperature. In particular, we provide results for
the particle density and the density-density correlator at the Mott transitions
and within the superfluid phase. For the former quantity, numerical outcomes
are also extensively compared to Local Density Approximation predictions.
