Anomaly detection for core temperature has great significance in maintaining the safety of nuclear power plants. However, traditional auto-encoder-based anomaly detection methods might extract the latent space features with redundancy, which may lead to missing and false alarms. To address this problem, the idea of feature disentangling is introduced under the auto-encoder framework in this paper. First, a feature disentangling auto-encoder (DAE) is proposed where a latent space disentangling loss is designed to disentangle the features. We further propose an incrementally feature disentangling auto-encoder (IDAE), which is the improved version of DAE. In the IDAE model, an incremental feature generation strategy is developed, which enables the model to evaluate the disentangling degree to adaptively determine the feature dimension. Furthermore, an iterative training framework is designed, which focuses on the parameter training of the newly incremented feature, overcoming the difficulty of model training. Finally, we illustrate the effectiveness and superiority of the proposed method on a real nuclear reactor core temperature dataset. IDAE achieves average false alarm rates of 4.745% and 6.315%, respectively, using two monitoring statistics, and achieves average missing alarm rates of 6.4% and 2.9%, respectively, using two monitoring statistics, outperforming the other methods.