Anomaly detection in industrial environments aims at detecting anomalies in the monitoring data of industrial machinery or equipment, as soon as possible, preferably presenting real-time alarms, to alert the monitoring staff and start maintenance activities timely. In this paper, the problem of anomaly detection of an industrial furnace is tackled, for the real-time recognition of punctual anomalies on multivariate time series. To this aim, a real-time anomaly detection approach is proposed: first, time series acquired from the real machinery are filtered, to select those of interest for possible anomalies, and pre-processed, to obtain sliding windows for real-time detection, then distinct univariate models are applied, to identify different anomaly types. For the application considered here, data regarding the machinery behaviour were available only for normal functioning, thus an unsupervised approach is chosen. In particular, deep learning models based on autoencoders are used to detect punctual anomalies, by reconstructing each window and evaluating the reconstruction error of its last point. An extensive set of autoencoder models is proposed, with varying architecture in terms of type of model (vanilla/variational autoencoders), type of layers (fully connected/LSTM/BiLSTM), and hyperparameters (number of layers, intermediate sizes, BiLSTM type). Available data are split, and used to train the models, and to test them on the normal signal and on synthetic anomalies injected on it, which are of particular interest and were designed according to domain experts. Performances of the proposed models show differences among them, depending on the model architecture. The most efficient models, in terms of F1 score of detection and number of parameters, are identified by their t-test comparison, and the capability of detecting anomalies online is demonstrated. In particular, the proposed anomaly detection approach, including a selected autoencoder with LSTM layers, is able to correctly recognize normal trends, with very few false positives, and promptly give alarms as different anomalous trends appear.