We study the emission line shapes of single CdSe nanocrystallite quantum dots. Single dot line shapes are found to result from rapid spectral shifting of the emission spectrum rather than the intrinsic physics of the quantum dot. A strong dependence of single dot line widths on excitation intensity, wavelength, temperature, and integration time is found and is correlated with the number of times that the quantum dot is excited during the acquisition of a single spectrum. The observed results are consistent with thermally assisted spectral diffusion activated by the release of excess excitation energy.