Various deep learning models have been developed for indoor localization based on radio-frequency identification (RFID) tags. However, they often require adaptation to ensure accurate tracking in new target operational domains. To address this challenge, unsupervised domain adaptation (UDA) methods have been proposed to align pre-trained models with data from target environments. However, they rely on large annotated datasets from the initial domain (source). Source data access is limited by privacy, storage, computational, and transfer constraints. Although many source-free domain adaptation (SFDA) methods address these constraints in classification, applying them to regression models for localization remains challenging. Indeed, target datasets for indoor localization are typically small, with few features and samples, and are noisy. Adapting regression models requires high-confidence target pseudo-annotation to avoid over-training. In this paper, a specialized mean-teacher method called MTLoc is proposed for SFDA. MTLoc updates the student network using noisy data and teacher-generated pseudo-labels. The teacher network maintains stability through exponential moving averages. To further ensure robustness, the teacher's pseudo-labels are refined using k-nearest neighbor correction. MTLoc allows for self-supervised learning on target data, facilitating effective adaptation to dynamic and noisy indoor environments. Validated using real-world data from our experimental setup with INLAN Inc., our results show that MTLoc achieves high localization accuracy under challenging conditions, significantly reducing localization error compared to baselines, including the state-of-the-art adversarial UDA approach with access to source data.