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We study the influence of temperature and the values of basic energy parameters on the character of vibron self-trapped states in quasi-one-dimensional hydrogen-bonded molecular chains. Investigations have been carried out within the one-dimensional Holstein molecular crystal model employing the variational extension of the Lang-Firsov unitary transformation. It was found that, in the low-temperature regime, only partially dressed small-polaron states may exist. With the rise of temperature, the system enters the metastability region, where partially dressed (light and mobile) and fully dressed (heavy and practically immobile) small-polaron states may exist simultaneously.