The relationship between climate change, a new source of financial risk, and the banking system is important for financial risk management and regulation. In this paper, we investigate the impact of temperature shocks on the systemic risk of Chinese listed banks, which is measured by a new nonlinear tail-event driven network (TENET) conditional value-at-risk (CoVaR) under g-expectation. We find that higher temperatures significantly increase the bank systemic risk, and the impact of temperature shocks is significantly larger during colder periods. The temperature shock can be regarded as a signal of bank systemic risk, which is necessary to maintain financial stability.