  We analyze the reorganization of free field theory correlators to closed
string amplitudes investigated in hep-th/0308184 hep-th/0402063 hep-th/0409233
hep-th/0504229 in the case of Euclidean thermal field theory and study how the
dual bulk geometry is encoded on them. The expectation value of Polyakov loop,
which is an order parameter for confinement-deconfinement transition, is
directly reflected on the dual bulk geometry. The dual geometry of confined
phase is found to be AdS space periodically identified in Euclidean time
direction. The gluing of Schwinger parameters, which is a key step for the
reorganization of field theory correlators, works in the same way as in the
non-thermal case. In deconfined phase the gluing is made possible only by
taking the dual geometry correctly. The dual geometry for deconfined phase does
not have a non-contractible circle in the Euclidean time direction.
