After a short historical review of the estimation theory from Gauss to Kalman, the MAP sequential estimator, a modern implementation of the deterministic Gauss approach, is compared with the discrete Kalman filter. The last one, owing to its statistical formulation, provides in general more reliable estimates because it takes into account the noise affecting the measured input variables (control functions) and the measured initial conditions. Both estimators are developed with n~ference to the 'problem of identification of temperature dependent thermophysical properties of materials from transient heat conduction data. Thermal conductivity and volumetric heat capacity are simultaneously reconstructed as a function of temperature using data of a single test. Several results of simulated experiments are analysed by means of two distinct methodologies, the Monte Carlo technique and the covariance analysis. The main characteristics of the algorithms are compared and the results show the better performance of the Kalman filter.