  The lineshape of spectroscopic transitions offer windows into the local
environment of a system. Here, we present a novel approach for connecting the
lineshape of a molecular exciton to finite-temperature lattice vibrations
within the context of the Davydov soliton model (A. S. Davydov and N. I.
Kislukha, Phys. Stat. Sol. {\bf 59},465(1973)). Our results are based upon a
numerically exact, self-consistent treatment of the model in which thermal
effects are introduced as fluctuations about the zero-temperature localized
soliton state. We find that both the energy fluctuations and the localization
can be described in terms of a parameter-free, reduced description by
introducing a critical temperature below which exciton self-trapping is
expected to be stable. Above this temperature, the self-consistent ansatz
relating the lattice distortion to the exciton wavefunction breaks down. Our
theoretical model coorelates well with both experimental observations on
molecular J-aggregate and resolves one of the critical issues concerning the
finite temperture stability of soliton states in alpha-helices and protein
peptide chains.
