The diffuse shape of the high-energy absorption band observed in oligothiophene crystals is interpreted in terms of Fano-type mixing between the discrete upper Davydov component at k = 0 and the continuum of phonon-accompanied exciton states at other values of crystal momentum. In temporal domain, this mixing is viewed as a crystal version of radiationless transition, and is followed by subsequent intra-band exciton relaxation due to scattering processes with phonon release. The rates of energy dissipation in these latter processes, mediated by different intramolecular vibrational modes, are estimated from a simple expression based on the Fermi golden rule. Depopulation of long-lived vibronic intermediates, acting as bottlenecks, is attributed to thermally activated processes with absorption of low-frequency phonons. All essential input parameters are obtained from independent nonempirical calculations. The results are in excellent agreement both with the experimentally observed absorption band shapes and with energy-dependent femtosecond dynamics afforded by measurements of sexithiophene (6T) fluorescence and photoinduced absorption.