A parametric study of a TESU (thermal energy storage unit), an essential component of a LAES (liquid air energy storage) system that stores a large amount of useful energy in an eco-friendly manner, is performed. The geometric conditions of the TESU cover the overall heat conductance, the volume, and the type of thermal energy storage material. The operating conditions of the TESU are defined by the operating time, the working mass, and the power generation pressure of the LAES system. The effectiveness is used as a thermal performance indicator of the TESU considered as a heat exchanger and a thermal battery. The heat capacities of the TESU and high-pressure working fluid, the overall heat conductance, the operating time of the TESU, and the maximum temperature span are selected as critical parameters. We calculate the effectiveness using the parameters in seventy-three different conditions. Based on the calculation results, this paper nondimensionalizes the parameters using the π theorem. This research paper presents a correlation between the obtained π groups and the effectiveness, which satisfies the Pearson correlation coefficient (PCC) of 0.82.