The transition from internal combustion to electrically powered vehicles (EVs) is accelerating, with some estimates predicting that 45% of new cars sold in the US will be fully electric by 2035. EVs will be powered by lithium-ion batteries (LIBs). This high-power application can subject LIBs to significant electrical, mechanical, and thermal abuse. Predicting and preventing thermal runaway (TR) is therefore of utmost importance to save lives and ameliorate the transition to renewable energy. Currently, battery management systems monitor cell voltage, current, temperature, and presence of gases, which does not provide sufficient advanced warning of a catastrophic event [J. Acoust. Soc. Am., 150, A66 (2021)]. This work explores the viability of evaluating cell safety by monitoring and interpreting ultrasonic signals propagating through a battery as it undergoes localized heating. We monitor different portions of received waveforms, linking them to specific propagating modes or multi-path arrivals. A finite element model is then used to understand the mode of propagation of the chosen frequencies, and the methodology is applied to both 10Ah and 60Ah cells. The time-domain features of signal amplitude and time-of-flight are used to create safety metrics which warn of TR as much as 25 min in advance of failure.