The real and imaginary components, C-p' and C-p", respectively, of the complex heat capacity, C-p* = C-p' - iC(p)", of a molecular liquid have been measured in the temperature range of its vitrification and in the glassy state, and the effect of spontaneous structural relaxation has been determined in real time. C-p' of the glassy state is found to decrease with time. Analysis shows that this is mainly due to the decrease of configurational entropy as the characteristic time of the C-p' spectra increases and consequently the contribution from the unfrozen, faster modes of the alpha-relaxation process decreases. There may also be a significant decrease in the vibrational and anharmonic force contributions as the glass densifies. Interpretations in terms of the potential energy landscape model suggest that for each state of lower energy attained with time, the number of minima in the potential energy surface decreases, and the minima become deeper.