A perturbation in the ratio of the matter temperature to the radiation temperature in the form of a Gaussian with amplitude A and width σ (in units of the redshift z) centered at some redshift z_c is considered, with some "standard" temperature ratio obtained from a simultaneous solution of the cosmological recombination kinetics and energy equations being taken as the initial (unperturbed) one. Comparatively small (A = ± 0.01), fast (σ = 17) perturbations are shown to give rise to distinct narrow absorption (for A > 0) or emission (for A < 0) quasi-lines in each of the subordinate continua. The positions of these quasi-lines correlate with the position of the perturbation center, while their intensities are very sensitive to the perturbation amplitude. At the same time, the manifestation of the perturbation is much less clear in hydrogen lines (subordinate ones and the Ly-α line) and two-photon emission. As a result, the full perturbed spectrum is characterized by the presence of the narrow quasi-lines mentioned above and by a general decrease (for A > 0) or increase (for A < 0) in intensity with increasing wavelength.