In olefin plants, good performance of the pyrolysis units is one of the key elements to efficient operation of the entire facility. In order to achieve efficient operation and lessen the burden of the operators, the on-line inference system of tube-wall temperature is required. In order to estimate the tube-wall temperature by using on-line measured process variables, a two step modeling approach: 1) building a physical model based on the first principles of chemical engineering: and 2) incorporating a statistical model with the physical model so as to improve the prediction accuracy for any operating conditions, is proposed. The statistical model was built by conducting a PLS (Partial Least Squares) analysis. Application of the proposed inference system, where the PLS model is integrated with the physical model, is illustrated using operating data obtained from industrial olefin pyrolysis plants. The results show that the proposed system can predict the tube-wall temperature successfully for almost all operating conditions.