We have studied the temperature dependence of the absorption spectra of soluble, conjugated polymers of known chain length (similar to 100-1000 double bonds), synthesized by Schattenmann [Macromolecules 29, 8990 (1996)] using living polymerization techniques. The polymer spectra show significant redshifts upon cooling from 300 to 80 K. To estimate the distributions of conjugated segments in these conformationally disordered samples, the spectra were fitted to a superposition of absorption spectra of conjugated segments of known lengths. These "experimental" distributions of conjugated segments then were compared to those predicted by theoretical models of conformational disorder. Although the low-temperature samples contain significant populations of long segments, the shortest polyene segments dominate all distributions. We compare these experimental results with distributions derived from the model of Yaliraki and Silbey [J. Chem. Phys. 104, 1245 (1996)]. Adjustment of relevant energy parameters gives good qualitative agreement between the experimental and theoretical distributions in long polyenes.