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

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... ck 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.