In the emergence of new technologies to harness renewable energy, industrial-scale storage of heated water in a geothermal system is a promising technique. A porous, permeable medium, bounded by a poorly thermally conductive/convective overburden and underburden, can be used for transient subsurface thermal storage. The reservoir in this concept forms a geothermal battery. As a very simplified scenario, consider a single well injecting and producing hot water diurnally or seasonally. The source of the hot water could be solar-heated water, for example, or possibly even water heated from the excess regional electricity supply. For that situation, this study investigates the influence of spatial permeability heterogeneity on heat recovery, and the distributions of temperature and pressure inside the reservoir. Four heterogeneous models are created from lognormal distributions of permeability by varying the standard deviations while keeping the mean absolute permeability at 100 mD. The injection pressure experienced while pumping into a candidate formation is affected by heterogeneity; higher bottom hole pressure is required to inject water into a more heterogeneous reservoir. The spatial distribution of temperature is less affected by permeability heterogeneity. In the simulations carried out, 91% of the heat is recovered after the 30 ${}^{\mathrm{th}}$ cycle of injection/production operation in all cases proving less impact of heterogeneity on heat recovery for fixed injection and production rates.