Uncertainties of cell temperature and aging are two challenges for the power management of battery-integrated systems. To evaluate the maximum power capability of batteries with uncertain degree of degradation and internal temperature, a temperature-compensated battery model is first established as a base model in this paper. Then the linear migration with particle filtering is employed to adjust the developed base model so that the migrated model can be adaptive to the uncertainties of aging and internal temperature. Moreover, a numerical seeking method is proposed for state of power (SoP) calculation to avoid direct handling of the complex, highly nonlinear battery model. After that, the multiple constraints such as current, state of charge (SoC), and voltage limitations are considered for SoP estimation. Experimental results show that for the cases of capacity degradation up to 15%, temperature variation up to 40 °C, and the root-mean-square error (RMSE) of the voltage measurement noise up to 50 mV, the RMSE of the voltage tracking for SoP calculation can still be limited to 8.4 mV, and the RMSE of the SoC estimation is better than 1.64%. In addition, the computational efficiency of the proposed seeking algorithm is stable with particle filters using different configurations.