Thermally regenerative ammonia batteries (TRABs) are an emerging technology that use low temperature heat (T < 150 °C) to recharge a flow battery that produces electrical power on demand. The all-aqueous copper TRAB can provide high power densities and thermal energy efficiencies relative to other devices that harvest energy from waste heat, but its performance is adversely impacted by the crossover of undesired species through the membrane and lower cell voltages compared to conventional batteries. In this work, we developed a numerical model to simulate discharge curves while accounting for crossover inefficiencies without tracking all electrolyte species through the membrane. The model was able to successfully reproduce discharge curves across a diverse range of battery conditions using a single fitting parameter to account for decay of electrode standard potential due to species crossover with minimal error (< 5%). The model was then used to simulate different design scenarios to estimate changes in energy output from alterations to the aspects of the battery electrolyte chemistry. Results from this study are used to identify pathways for improving future TRAB designs with respect to energy capacity and cost-effectiveness of the technology.