Fault diagnosis of rolling bearings is a crucial task in Prognostics and Health Management, as rolling elements are ubiquitous in industrial assets. Data-driven approaches based on deep neural networks have achieved great progress in this area. However, they require the collection of large representative labeled data sets. Yet, industrial assets are often operated in working conditions different from the one in which the labeled data have been collected, requiring a transfer between working conditions. In this work, we tackle classification of bearing fault types and severity levels under varying operating conditions, in the setting of unsupervised domain adaptation (UDA), where labeled data are available in a source domain and only unlabeled data are available in a different but related target domain. In self-training UDA methods, based on pseudo-labeling of target samples, one major challenge is to avoid error accumulation due to low-quality pseudo-labels. Most such methods select pseudo-labels based on their prediction confidence. However, it is well known that pseudo-labels are often over-confident and badly calibrated in the target domain. In this work, we aim to address these challenges and propose to incorporate post-hoc calibration, such as the well-known temperature scaling, into the self-training process to increase the quality of selected pseudo-labels. We propose calibrated versions of two self-training algorithms, Calibrated Pseudo-Labeling and Calibrated Adaptive Teacher, achieving competitive results on the Paderborn University (PU) benchmark.