Detecting local heat-dissipating zones in high-temperature superconductor (HTS) magnets is a challenging task due to slow propagation of such zones in HTS conductors. For long conductor lengths, voltage-based methods may not provide a sufficient sensitivity or redundancy, and therefore nonvoltage-based detection alternatives are being sought. One of those is the recently proposed method of Eigen Frequency Thermometry (EFT), which is an active acoustic technique for a fast and nonintrusive detection of 'hot spots,' utilizing temperature dependence of the conductor elastic moduli. In this work, we demonstrate the efficiency of EFT for detecting localized heating in a 1.2-m-long sample of REBCO tape immersed in liquid nitrogen, and benchmark sensitivity of the acoustic detection with respect to voltage, hot spot temperature, and power dissipation in the conductor. Modifying the original technique for differential mode of operation enables a much improved sensitivity, and adds a hot spot localization capability. Furthermore, we adapt this technique to subscale coils wound with REBCO CORC conductor built in the framework of U.S. Magnet Development Program. A successful thermal-based detection of dissipation onset at the critical current for a two-layer canted CORC dipole assembly is discussed.