Terminologies of specialized problem domains present an important part of knowledge to be extracted for various applications, such as construction of thesauri, ontologies, glossaries and so on. Meanwhile, widely-used automatic term extraction (ATE) methods are mainly statistics-based and show quite average quality, so ways to leverage modern deep learning techniques are currently studied. The paper addresses the task of term recognition based on BERT classifier of term candidates previously extracted from text; cross-domain settings are considered for training BERT models. The dataset constructed for experiments is presented, which contains samples taken from scientific texts in Russian. The results of the experiments with cross-domain term recognition are described, demonstrating comparable or slightly better quality than the most known ATE methods.