Sodium acetate trihydrate (SAT), due to its high enthalpy value during exothermic decomposition reactions, has emerged as a potential candidate for chemical energy storage materials. However, there remains a lack of convenient and accurate prediction methods for calculating temperature and energy storage progress of SAT. This study aims to develop a fast chart-lookup strategy for chip thermal management systems with SAT using machine learning, which utilizes existing complex reaction kinetics models. Specifically, we extensively collected training data corresponding to various operating conditions such as material thermal properties, heat source power, and time from model calculations. And dimensionality reduction techniques were used to consolidate numerous variables that affect heat transfer rates into a single variable: characteristic time, which helps to extract principal components for visualizing machine learning results. Then we utilized back propagation (BP) neural networks to identify the relationship between characteristic time, energy storage progress, and temperature from the training dataset, which is plotted on the chart. The R-values for the training outcomes all exceeded 0.999, ensuring reliability across most thermal management scenarios. With the chart-lookup strategy generated by machine learning, engineers can now use a pocket calculator and charts to estimate the working temperature and progress of SAT within minutes, as well as predict system parameters and appropriate material properties based on temperature requirements, rather than relying on hours of simulation calculations.