Retrieving an accurate battery's state-of-charge (SOC) is crucial for reliable operation in a variety of use cases as the era of vehicle electrification advances. Traditional methods of state-of-charge estimation often struggle with the underlying non-linear behavior and the battery's temperature effect on the estimation's accuracy. This work suggests a model-based method using the Extended Kalman Filter to estimate the battery's state-of-charge under multiple tests while accounting for the temperature effect to improve its robustness and accuracy. The testing dataset from the Tesla Model 3 NCA Li-ion battery, which McMaster University made available online, supports the study. The methodology starts with developing a second-order continuous dual-polarization (DP) equivalent circuit model.