Langasite (LGS), langatate (LGT), and similar piezoelectric crystals in the P321 crystal class have become an increasing focus of research during the past two decades, and much of the motivation for this research has been the application of these materials in high-temperature resonant acoustic sensing. The quality factor Q of these materials directly affects the resolution of sensors, and Q decreases dramatically at elevated temperatures. We present measurements and multi-frequency least-squares analysis of Q -1 of LGS and LGT bulk-acoustic resonators as a function of temperature that reveal a superposition of physical effects contributing to the damping, including point-defect relaxations and intrinsic phonon-phonon loss. In LGS, these effects are superimposed on a background that increases with increasing temperature. Parameters for this background obtained from least-squares analysis are found to be consistent with an anelastic dislocation mechanism with a distribution of activation energies. The absence of a significant background of this type in LGT, over the measured temperature range, and associated differences in the crystal growth and phase diagrams of LGS and LGT provide support for the view that LGT is a more attractive choice for high-temperature sensing applications.