We have measured the time-integrated fluorescence of coumarin 153 in a glass-forming solvent in order to assess the inhomogeneous linewidth as a function of temperature. A maximum of this width is observed at a temperature where the structural relaxation time of the solvent matches the excited state lifetime of the dye of a few nanoseconds. This feature can be explained only on the basis of a relaxation time dispersion which originates from a spatial distribution of solvent response times. Therefore, liquid dynamics in the regime of nanosecond time scales are heterogeneous with respect to the structural relaxation time.