Efficient prediction of thermal system performance is crucial for optimizing building energy systems. This paper introduces a predictive model to forecast Heating, Ventilation, and Air Conditioning (HVAC) systems' performance with Ice Thermal Energy Storage (ITES). The indicators encompass storage temperature, Coefficient of Performance (COP), cooling thermal load, and chiller power consumption. These forecasts play a pivotal role in cost-effective experimentation, energy optimization, reduced consumption, and minimized operational costs. The study focuses on developing an Artificial Neural Network (ANN) model using a shallow Neural Net Fitting application (nftool). This ANN model predicts necessary ITES system configurations based on nonlinear input variables. Utilizing a comprehensive dataset, incorporating dry bulb temperature, component inlet and outlet temperatures, flow rates, and control valve states, the ANN model is built and validated. Performance metrics, including Mean Squared Errors (MSE) and Regression (R), are employed for training, validation, and testing to predict individual configurations. The results reveal R values ranging from 0.94 to 0.99, with MSE mostly below 20 %. This study exemplifies machine learning's application to ITES cooling systems, serving as a benchmark for evaluating ANN methodologies' effectiveness in prediction. It sheds light on parameter variation's impact on ITES cooling systems and underscores ANN's accuracy in predicting HVAC system parameters with ITES.