Data-based modeling is utilized for the dynamic estimation of the temperature inside a solid oxide fuel cell (SOFC) stack. Experiment design and implementation, data pretreatment, model parameter identification and application of the obtained model for the estimation and prediction of the SOFC stack maximum and minimum temperatures are covered. Experiments are carried out on a complete 10 kW SOFC system to obtain data for model development. An ARX-type (autoregressive with extra input) polynomial input output model is identified from the data and Kalman filtering is utilized to obtain an accurate estimator for the internal stack temperatures. Prediction capabilities of the model are demonstrated and using the modeling approach for SOFC system monitoring is discussed. (C) 2014 Elsevier B.V. All rights reserved.