We propose a one-dimensional hydrogen-bonded chain model, where temperature is introduced using a variational form of the SCPA method to evaluate the semi-quantum free energy. The parameters of the model are chosen self-consistently and the hydrogen bond is described by a double Morse interaction. The behaviour of the chain is studied with a defect and without one and the Peierls barrier is calculated. Introduction of an anharmonic O-O interaction results in slight qualitative changes.