  Using a model of Frenkel excitons coupled to a bath of acoustic phonons in
the host medium, we study the temperature dependence of the dephasing rates and
homogeneous line width in linear molecular aggregates. The model includes
localization by disorder and predicts a power-law thermal scaling of the
effective homogeneous line width. The theory gives excellent agreement with
temperature dependent absorption and hole-burning experiments on aggregates of
the dye pseudoisocyanine.
