In this paper, a non-linear controlled autoregressive autoregressive moving average (N-CARARMA) model was developed using extended least square algorithm (ELS) and extended stochastic gradient algorithm (ESG) to predict the evolution of the overhead temperature of a distillation column system. The model parameters were estimated and verified by taking input and output data from the separation unit under nominal operating conditions. Three criteria of models selection: Akaike’s Information Criterion (AIC), Root Mean Square Error (RMSE), and Nash-Sutcliffe Efficiency (NSE) are used to estimate the prediction performance of the N-CARARMA model. Using real experimental data, it is showed that the best structure of the proposed model can be used to describe the overhead temperature at different nominal operating conditions.