The aim of the presented investigation is to explore the time gap between an anomaly appearance in continuously measured parameters of the device and a failure, related to the end of the remaining resource of the device-critical component. In this investigation, we propose a recurrent neural network to model the time series of the parameters of the healthy device to detect anomalies by comparing the predicted values with the ones actually measured. An experimental investigation was performed on SCADA estimates received from different wind turbines with failures. A recurrent neural network was used to predict the temperature of the gearbox. The comparison of the predicted temperature values and the actual measured ones showed that anomalies in the gearbox temperature could be detected up to 37 days before the failure of the device-critical component. The performed investigation compared different models that can be used for temperature time-series modeling and the influence of selected input features on the performance of temperature anomaly detection.