We report a thorough computational characterization of the low- and room-temperature absorption and emission spectra of a series of oligothiophenes that contain between three and seven thiophene units. Our computational approach is based on time-dependent (TD) density functional calculations with the CAM-B3LYP functional. The effect of vibrations is included without resorting to any empirical parameters either at a fully quantum level or with a hybrid quantum-classical protocol. This latter approach is introduced to describe the relevant broadening effects in absorption at room temperature and is based on the partition of the vibrational modes into two sets: the inter-ring torsions treated at the anharmonic level in a classical way and the remaining modes described at the quantum level. The contribution of the quantum modes to the spectrum is computed by using a harmonic approximation, which accounts for Duschinsky mixing and changes in the vibrational frequencies associated with the electronic transition; a path-integral TD approach is adopted to account for the effect of temperature. The spectra simulated at low temperatures are in very good agreement with their experimental counterparts, which indicates that our calculations can quantitatively reproduce the effect of chain lengthening on the position and the shape of the spectra. Good agreement is also obtained at room temperature, for which we show that the classical description of the broadening, owing to the inter-ring torsions, reproduces the loss of the vibronic structure observed in the experiment and introduces only a slight overestimation of the spectral width.