We propose a one-dimensional hydrogen-bonded chain model, where temper
ature is introduced using a variational form of the SCPA method to eva
luate the semi-quantum free energy. The parameters of the model are ch
osen 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 o
f an anharmonic O-O interaction results in slight qualitative changes.