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We formulate the finite temperature theory for the free thermal excitationsof the bosonic string in the anti-de Sitter (AdS) spacetime in the Thermo FieldDynamics (TFD) approach. The spacetime metric is treated exactly while thestring and the thermal reservoir are semiclassically quantized at the firstorder perturbation theory with respect to the dimensionless parameter $\epsilon= \a ' H^{-2}$. In the conformal $D=2+1$ black-hole AdS background thequantization is exact. The method can be extended to the arbitrary AdSspacetime only in the first order perturbation. This approximation is taken inthe center of mass reference frame and it is justified by the fact that at thefirst order the string dynamics is determined only by the interaction betweenthe {\em free} string oscillation modes and the {\em exact} background. Thefirst order thermal string is obtained by thermalization of the $T = 0$ systemcarried on by the TFD Bogoliubov operator. We determine the free thermal stringstates and compute the local entropy and free energy in the center of massreference frame.Comment: Minor typos corrected. Two references added. LATeX file, 19 page

First order semiclassical thermal string in the AdS spacetime