The internal battery parameters of the lithium-ion battery (LIB) energy storage system may be inconsistent due to different aging degrees during the operation, and the thermal effect can also threaten the safety of the system. In this paper, based on the second-order resistor-capacitor (2-RC) equivalent circuit model (ECM) and the dual extended Kalman filter (DEKF) algorithm, an electrical simulation model of a LIB pack with inconsistent parameters considering the thermal effect is established, in which state of charge (SOC) and state of health (SOH) are estimated using DEKF while the temperature is calculated by a thermal module. The simulation results show that the DEKF algorithm has a good effect on battery state and parameter estimation, with the root mean square error (RMSE) of voltage is lower than 0.01 V and SOC mean average error (MAE) is below 1.50 % while SOH error is 3.37 %. In addition, the thermal module can provide an accurate estimation on the inconsistent temperature rise of the battery pack, and the MAE between the model-calculated temperature and the experiment is no more than 6.60 %. This paper provides the basic data for the scale-up of the electrothermal co-simulation model of the LIB energy storage system.