The ability of L-glutamic acid to crystallize in two different forms has long been the subject of study due to its commercial importance. While a solvent-mediated phase transformation between the alpha and beta polymorphs is the prevailing theory, recent reports indicate a thermal solid-solid transformation between the two may be possible. However, determining accurate thermodynamic stabilities of these crystals has been challenging. Here new low-temperature single-crystal X-ray diffraction data coupled to solid-state density functional theory simulations have enabled a detailed description to be achieved for the energetic parameters governing the stabilization of the two L-glutamic acid solids. The temperature-dependent Gibbs free-energy curves show that alpha-glutamic acid is the preferred form at low temperatures (<222 K) and the beta form is most stable at ambient temperatures. Terahertz time-domain spectroscopy was utilized to evaluate the quality of the intermolecular force modeling as well as to provide characteristic low-frequency spectral data that can be used for quantification of polymorph mixtures or crystal growth monitoring.