The excess energy dissipation process of photoexcited S-1 trans-stilbene in solution has been studied with picosecond time-resolved Raman spectroscopy. The peak position of the 1570-cm(-1) band (C=C stretch) is shown to be useful as an indicator of picosecond temperature changes; a picosecond time-resolved Raman spectrometer can be regarded as a "picosecond Raman thermometer". The cooling rates of S-1 trans-stilbene thus observed in 10 different solvents show a strong correlation with the thermal diffusivities of the bulk solvents. Based on this observation, a simple numerical model is proposed for the solute-solvent energy dissipation process in solution. The observed cooling kinetics are analyzed with this macroscopic model. It is concluded that the excess energy is first shared among the solute and the nearest solvent molecules in a few picoseconds or faster. The further heat conduction to outer-sphere solvent molecules determines the whole dissipation rate, which explains the observed correlation between the vibrational cooling rate and the thermal diffusivity of the solvent.