Thermal runaway of lithium-ion batteries evolves rapidly and causes severe hazards, making it a critical safety risk for the safe operation of energy storage systems. Conventional fixed-threshold warning methods usually trigger alarms only after the system state has significantly deviated from normal conditions, making it difficult to balance warning lead time and false alarm control. Moreover, variations in operating conditions and cell-to-cell differences may lead to scale drift in anomaly scores, thereby weakening the consistency of fixed-threshold decisions. To address these problems, a risk-mapping and persistent-triggering decision framework for thermal runaway warning in energy storage systems, namely persistent triggering, risk mapping, input representation, multi-stage evaluation, and engineering deployment for thermal runaway (PRIME-TR) was proposed. Without adding extra sensors, the framework only relied on multivariate time-series data available from the battery management system. Through a three-stage structure of "anomaly perception-risk mapping-persistent triggering", raw anomaly scores were transformed into risk scores with quantile semantics, and persistent-triggering constraints were introduced at the decision layer to generate more stable warning outputs. In dynamic stress test, federal urban driving schedule, and cross-cell validation scenarios, PRIME-TR produced no false alarms under fixed-threshold conditions. Unified evaluation results based on thermally induced failure experiments from the NLR battery failure databank show that PRIME-TR achieves a warning lead time of 0.366 7 min, approximately 22 s, relative to the reference time of sustained irreversible structural propagation inside the cell, outperforming temperature threshold, voltage threshold, EWMA, Isolation Forest, PCA-T², and COPOD. Further virtual cabinet parallel experiments show that, at a system scale of N=500, the proposed framework can still maintain controllable system-level false alarms and suppress false alarm amplification caused by synchronous transient disturbances through decision-layer temporal gating. The results indicate that PRIME-TR improves the consistency of risk decisions and the stability of warning outputs without changing the underlying detector, providing a deployable decision-layer solution for online thermal runaway warning in energy storage systems.