The cooling of p-nitroaniline (PNA), dimethylamino-p-nitroaniline (DPNA) and trans-stilbene (t-stilbene) in solution is studied experimentally and theoretically. Using the pump-supercontinuum probe (PSCP) technique we observed the complete spectral evolution of hot absorption induced by femtosecond optical pumping. In t-stilbene the hot S-1 state results from S-n-->S-1 internal conversion with 50 fs characteristic time. The time constant of intramolecular thermalization or intramolecular vibrational redistribution (IVR) in S-1 is estimated as tau (IVR)<<100 fs. In PNA and DPNA the hot ground state is prepared by S-1-->S-0 relaxation with characteristic time 0.3-1.0 ps. The initial molecular temperature is 1300 K for PNA and 860 K for t-stilbene. The subsequent cooling dynamics (vibrational cooling) is deduced from the transient spectra by assuming: (i) a Gaussian shape for the hot absorption band, (ii) a linear dependence of its peak frequency nu (m) and width square Gamma (2) on molecular temperature T. Within this framework we derive analytic expressions for the differential absorption signal Delta OD(T(t),nu). After calibration with stationary absorption spectra in a low temperature range, the solute temperature T(t) may be evaluated from a transient absorption experiment. For highly polar PNA and DPNA, T(t) is well described by a biexponential decay which reflects local heating effects, while for nonpolar t-stilbene the local heating is negligible and the cooling proceeds monoexponentially. To rationalize this behavior, an analytic model is developed, which considers energy flow from the hot solute to a first solvent shell and then to the bulk solvent. Fastest cooling is found for PNA in water: a time constant of 0.64 ps (68%) corresponds to solute-solvent energy transfer while 2.0 ps (32%) characterizes the cooling of the first shell. In aprotic solvents cooling is slower than in alcohols and slows down further with decreasing solvent polarity. This contrasts with nonpolar t-stilbene which cools down with 8.5 ps both in acetonitrile and cyclohexane. Comparison of the cooling kinetics for PNA in water with those for DPNA in water-acetonitrile mixtures suggests that the solute-solvent energy transfer proceeds mainly through hydrogen bonds.