The temperature and laser-power dependent S-1 <-- S-0 spectra of single diphenyloctatetraene molecules in n-tetradecane are investigated using one- and two-photon excitation at cryogenic temperatures. Under one photon excitation, the single-molecule transitions shift to lower frequencies and the line widths increase with increasing temperature while the line shapes are independent of the laser power up to spectral saturation. The experimental data are consistent with the model of thermal activation of a single local phonon. Under two-photon excitation, the transitions shift linearly to lower frequencies with increasing laser power while the lines broaden only weakly. These results are discussed in terms of laser-induced ac-Stark shifts and matrix dynamics. In particular, a bottleneck effect in the thermalization of nonequilibrium phonons is supposed to play an essential role in the observed broadening and shifts. The comparison of one- and two-photon excitation spectra provides information about the processes that govern the two-photon spectra.