Are spectra (both fluorescence and absorbance) of any molecule dependent on temperature?
The characteristic wavelengths do not change with temperature but the intensities will. As temperature changes, the relative concentrations of molecules with particular energy levels will change and that will affect the relative strength of absorption bands and the relative intensity of fluorescence lines.
This effect is particularly obvious if, say, the rising temperature causes a molecule to dissociate. This would cause the spectral features of the molecule to become less important while the spectral features of its dissociation products become more important.
Even without dissociation, temperature effects in fluorescence or absorption are readily observed in gases. The concentrations of rotational states of molecules will change with temperature and this will affect both fluorescence and absorption features.
is the spectral lineshape function of any molecule dependent on the temperature...?
Higher temperatures cause greater broadening of lines. This effect is often negligible but it can be the dominant broadening mechanism in low-pressure gases. This effect is called doppler broadening.