The optical absorption spectrum in an analytically solvable model of a localized-electron and phonons is investigated using the operator algebra in NonEquilibrium Thermo Field Dynamics (NETFD). The position and the curvature of the adiabatic potentials for the ground and for the excited electronic states are assumed to differ from each other. The structures of the absorption spectra are investigated for various situations including the cases of slow modulation and of fast one. The method of NETFD is explained in order to be self-contained in solving the problem.