All-solid-state batteries are often assumed to be safer than conventional Li-ion ones. In this work, we present the first thermodynamic models to quantitatively evaluate solid-state and Li-ion battery heat release under several failure scenarios. The solid-state battery analysis is carried out with an Li7La3Zr2O12 solid electrolyte but can be extended to other configurations using the accompanying spreadsheet. We consider solid-state batteries that include a relatively small amount of liquid electrolyte, which is often added at the cathode to reduce interfacial resistance. While the addition of small amounts of liquid electrolyte increases heat release under specific failure scenarios, it may be small enough that other considerations, such as manufacturability and performance, are more important commercially. We show that short-circuited all-solid-state batteries can reach temperatures significantly higher than conventional Li-ion, which could lead to fire through flammable packaging and/or nearby materials. Our work highlights the need for quantitative safety analyses of solid-state batteries.