Due to their high energy consumption and inherent thermal storage capacity, air conditioning loads have become key resources in source-load interaction. As a foundation for assessing flexible potential, non-intrusive load monitoring (NILM) enables the extraction of air conditioner operating information using only aggregate meter data. However, existing monitoring models not only struggle to capture the complex operating behaviors of air conditioners, but also rely heavily on hard-to-obtain power consumption labels when transferred from a source domain with training data to a new user in the target domains. To address these issues, a model-data hybrid-driven air conditioner monitoring and domain adaptation method is proposed. First, an air conditioner monitoring model integrating long- and short-term correlations between electrical and environmental features is developed. Second, a neural network is employed to identify thermodynamic parameters of air conditioners, enabling indoor temperature estimation. A temperature estimation loss is alternately embedded during training to fully exploit the strong correlation between air conditioner operation and indoor temperature. Finally, the physical model serves as a bridge for domain adaptation in new users, where easily accessible temperature data are used as supervisory signals to adapt to new data distribution. Experiments on both public and self-collected datasets demonstrate that the proposed method outperforms existing approaches in monitoring accuracy, transferability, and domain adaptability, showing promising potential for real-world applications.