The decay of a spatial transient temperature grating created within the molecular glass former phenolphthalein-dimethylether (PDE) relates to the hydrodynamic heat diffusion and the dynamics of local density fluctuations. The characteristics of the latter process agree well with the structural alpha relaxation observed by photon correlation and dielectric spectroscopy near and above the glass transition temperature T-g. When the alpha-relaxation time approaches the experimental timescale set-in by the thermal diffusivity the specific heat undergoes a dispersion. In either side of this dynamic regime, heat diffusion and alpha relaxation are independent modes. "Two fluid" models of the vitreous state conform to the experimental observations.