Phase change materials (PCMs) play a significant role in achieving sustainable objectives for green buildings. Organic solid–liquid PCMs have excellent heat energy storage density and suitable working temperatures, making them a focal point of research attention. However, these materials face challenges such as potential leakage, low thermal conductivity, and limited fire resistance, which hinder their direct application in the construction industry. Therefore, mineral-based PCMs are highly regarded due to their safety features, environmental friendliness, non-toxicity, and cost-effectiveness within sustainable building development. In this work, a multistage porous kaolinite-based geopolymer encapsulation material using primary raw materials like kaolinite mineral, sodium silicate surfactants, and hydrogen peroxide was successfully synthesized. The PEG is used as the organic solid–liquid PCM while natural graphite mineral serves as a heat transfer enhancement agent to fabricate a novel and sustainable mineral-based composite PCM, which could be applied at the environment temperature from 35–60 °C approximately. Furthermore, a study on material properties was conducted to investigate influencing factors. Comprehensive experimental reform on mineral-based PCMs will offer proficiency in experimental operations and foster the talents’ capacity for comprehensive design, which holds immense significance for understanding and designing mineral materials. This work holds great significance for the sustainable development for education and green buildings.