Maintenance is a crucial aspect of the process industry affecting economic and efficiency losses. Among different approaches, predictive maintenance allows for anticipating failure, thus reducing downtime. This work explores a data-driven approach to predictive maintenance by comparing the performance of two different statistical models in extrapolating the future performance of an industrial furnace. The models of interest are a polynomial regression model and a Gaussian process regression model, compared using rolling cross-validation. Moreover, three different machine learning techniques were compared during the training phase: cross-validation, ensemble method and train/test split. The models were trained on real-time series data collected from the distributed control system of a refinery plant. The best performance was obtained with the Gaussian process regression model trained with a train/test split approach. The resulting model can satisfactorily extrapolate the performance of a process furnace over a relatively short-term period.