The integration of phase change material (PCM) into building envelopes can effectively regulate indoor temperature fluctuations and reduce building energy consumption. However, passive PCM-integrated walls cannot be actively controlled. As an innovative application of flexible envelope system, active phase change wall (APW) enable active control of the wall's thermal performance by integrating phase change material (PCM) with a cold water piping system. However, the complexity of thermal inertia and heat transfer processes poses a challenge in quickly predicting the thermal responsiveness of the system. In this study, a methodology for predicting the indoor thermal response of APW using machine learning is proposed to quickly and accurately predict the APW thermal storage process and offer a solution for the control of intelligent flexible envelope system. Comparing the predictive accuracy and extrapolative performance of three shallow machine learning models (random forest, support vector machines, and extreme learning machines) with six advanced deep learning models (long shortterm memory, gated recurrent units, convolutional neural networks, and three type of Transformer-LSTM models). The machine learning models were trained using data from scaled experimental platforms. Results show that while machine learning models have a slight advantage in accuracy on training and test sets, deep learning models perform better in extrapolative tests. Notably, the Transformer-LSTM model improved the R2 value by 13.64 % compared to the random forest model in extrapolative tests, with corresponding reductions in mean absolute error by 70.75 %, mean absolute percentage error by 68.89 %, and root mean square error by 65.05 %. Implementing intelligent control strategy enables a 21.1 % increase in APW thermal regulation capacity while reducing thermal load leveling (TLL) by 0.96 %.