In recent years, voice-controlled personal assistants have revolutionized the interaction with smart devices and mobile applications. The collected data are then used by system providers to train language models (LMs). Each spoken message reveals personal information, hence removing private information from the input sentences is necessary. Our data sanitization process relies on recognizing and replacing named entities by other words from the same class. However, this may harm LM training because privacy-transformed data is unlikely to match the test distribution. This paper aims to fill the gap by focusing on the adaptation of LMs initially trained on privacy-transformed sentences using a small amount of original untransformed data. To do so, we combine class-based LMs, which provide an effective approach to overcome data sparsity in the context of n-gram LMs, and neural LMs, which handle longer contexts and can yield better predictions. Our experiments show that training an LM on privacy-transformed data result in a relative 11% word error rate (WER) increase compared to training on the original untransformed data, and adapting that model on a limited amount of original untransformed data leads to a relative 8% WER improvement over the model trained solely on privacy-transformed data.