Estimation of the surface temperature of a continuous aluminum cylindrical blank has been simulated in the process of heating under conditions where the statistical characteristics of the object noise and measurement noise are known a priori. A linear model of an object with distributed parameters was replaced by a seven-order model with lumped parameters. It is shown that such a replacement under given conditions yields a satisfactory precision and the model retains the properties of controllability and observability. To construct an observer based on a Kalman filter, special functions of the MATLAB medium have been employed. It has been found that for a wide range of dispersions of the measurement noise and control noise the precision of the temperature estimates over the cross sections of the blank are quite satisfactory.