The purpose of this study was to analyze the addition of phase-change materials to foamed geopolymer materials. Phase-change materials are compounds, or groups of compounds, that are capable of accumulating, absorbing, and losing energy at the phase transformation temperature. By weight, 5–15% of MikroCaps (MikroCaps, Slovenia), GR42, and PX25 (Rubitherm, Germany) were introduced as phase change materials. Geopolymer materials were produced based on fly ash with the addition of ash microspheres. The geopolymer composites were prepared using hydrogen peroxide, H2O2, Portland cement stabilizer, and a surfactant. The curing process of the geopolymer foams was carried out at 60 °C. The materials produced were tested for physical, mechanical, and thermal properties. The study included an analysis of the base material oxide composition, a particle size analysis of the phase change additives, and a determined the density of the composites and their structure. Thermal properties were studied in the temperature ranges of 0–20 °C, 20–40 °C, and 30–50 °C, while the specific heat was studied between 27.5 and 32.5 °C. The addition of phase-change materials to the geopolymer material increases the specific heat and the compactness of the phase-change material, but these values vary depending on the form of phase-change material used. With the introduction of PCM, it is possible to increase the heat capacity by up to 54% compared to samples without the addition of PCM. The effect phase-change materials have on strength properties also varies, with a reduction observed at low modifier densities. However, adding 10–15% increases strength by up to 30%. The obtained results show the strong potential of using geopolymers containing phase-change material additives within the construction industry. They could be used as insulating materials as they have strong insulating properties and accumulate heat very well.