Transient grating (TG) spectroscopy is an important experimental technique to measure mean-free-path (MFP) spectra using observations of quasiballistic heat conduction. To obtain MFP spectra, the measurements must be interpreted within the framework of the frequency-dependent Boltzmann transport equation (BTE), but previous solutions have restricted validity due to simplifying assumptions. Here we analyze heat conduction in TG using a new analytical solution of the frequency-dependent BTE that accurately describes thermal transport from the diffusive to ballistic regimes. We demonstrate that our result enables a more accurate measurement of MFP spectra and thus will lead to an improved understanding of heat conduction in solids.