The probability of failure of the battery system in a nuclear power plant is investigated under the assumption of total loss of ac power. This failure is the result of overheating of the battery cells due to the loss of ventilation that follows ac blackout (environmental common cause failure). The temperature of each cell and the design limit temperature are treated as random variables, and failure is assumed to occur when the former exceeds the latter. The distributions of these random variables are assessed using a simple thermal model, available data, and engineering judgment.