Lithium-Ion batteries (LIB) store energy for many different applications, especially in the mobility and smart grid areas. LIB has several advantages like stability, longer lifetime, and capacity compared with other technologies. Although, LIB can be dangerous, mainly if it operates in unsafe conditions due to failures that can appear and cause accidents like explosions or fire. To maintain the safe operation, an electronic system named Battery Management System (BMS) manages and controls the main parameters to guarantee the safe operation of the LIB. Therefore, BMS collects and controls the main parameters of the LIB like the voltage, current, and temperature. Despite that, BMS has challenges predicting, preventing, and identifying unforeseen failures. How a failure can be considered an anomaly, data-driven models can identify a precocious potential failure. For this reason, this paper presents an anomaly detection system to identify an overheating failure in a LIB as earlier as possible. A LIB prototype was built to simulate the overheating failures, and three anomaly detection algorithms have been applied to drive the work. An edge-cloud computing architecture collected and stored the needed data in a dataset to elaborate the idea and demonstrate the excellent results to anticipate failures in LIB. For future works, the intention is to operate with this approach in online embedded in the vehicle with the BMS to detect a failure precociously.