Industrial freezing is an energy-intensive process which is growing due to the increasing demand. This is exerting stress on electrical grids, especially at peak hours. To tackle this issue, thermal energy storage has received attention; however, there is a gap in terms of suitable materials for thermal energy storage with temperatures below -40 °C commonly needed in these applications. The solid-liquid phase change of carbon dioxide has the potential to be conceptually considered for thermal energy storage in a special type of heat exchangers known as pillow plate heat exchangers. Characteristically, these heat exchangers can withstand very high pressures which is a technical requirement for carbon dioxide thermal energy storage. This dataset includes the data and figures related to the concept of thermal storage in the solid-liquid transition of carbon dioxide.