(eng): This study aims at an extension and substantial improvement of the recently published relay-feedback parameter identification of an infinite-dimensional system thermal process model. The original procedure\nhas applied the standard on/off relay to get a simplified model. Then, the dominant pole assignment has given rise to the process model characteristic quasi-polynomial via the Levenberg-Marquardt algorithm.\nFinally, the same optimization tool has been used to determine transfer function numerator parameters. On the contrary, a saturated relay is used to receive an improved initial simplified-model estimation in this\ncontribution. As the process model in question has eight unknown parameters, a doubled relay test with artificial delay is made, which enables the estimation of all the parameters simultaneously. Moreover, the\nNelder-Mead algorithm is used as the optimization tool. A numerical example validates an enhanced estimation in time and frequency domains.