An incremental capacity parametric model for batteries is proposed. The model is based on Verhulst’s logistic equations and distributions in order to describe incremental capacity peaks. The model performance is compared with polynomial models and is demonstrated on a commercial lithium-ion cell. Experimental data features low-current discharges performed at temperatures ranging from −20 °C to 55 °C. The results demonstrate several advantages of the model compared to empirical models. The proposed model enables a clear description of the geometric features of incremental capacity peaks. It also doubles as an open circuit voltage model as the voltage curve can be fully recovered from parameterization on incremental capacity curves. The study of temperature sensitivity show that peak geometric parameters can be modelled as a function of temperature. An example of practical application is then displayed by using the model to estimate battery state-of-charge from voltage and temperature measurements. This example can expand to other practical applications for battery management systems such as state-of-health monitoring.