  In this paper we analyze the local localization of gravity in $AdS_4$ thick
brane embedded in $AdS_5$ space. The 3-brane is modelled by domain wall
solution of a theory with a bulk scalar field coupled to five-dimensional
gravity. In addition to small four-dimensional cosmological constant, the
vacuum expectation value (vev) of the scalar field controls the emergence of a
localized four-dimensional quasi-zero mode. We introduce high temperature
effects, and we show that gravity localization on a thick 3-brane is favored
below a critical temperature $T_c$. These investigations suggest the appearance
of another critical temperature $T_*,$ where the thick 3-brane engenders the
geometric $AdS/M/dS$ transitions.
