This article was motivated from a practical work on modeling and control of a time-delayed thermal airflow process using adaptive techniques. The work was divided into two parts: (I) the modeling of the process using system identification methods, with main concerns to the numerical robustness of the identification, and (II) the digital control of the process using adaptive self-tuning control, with main concerns to the adaptation of the controller to changes in the process dynamics. This article presents the first part of the work. The thermal airflow system was represented by an ARMAX model, whose parameters were identified using the Recursive Least Squares method, based on two approaches: the Matrix Inversion Lemma, and the Bierman’s UD Factorization. The results obtained show that the last approach has greater numerical robustness and is more suitable for applications of adaptive control – the second part of the work, described in a separate article.