Temperature and cell aging are two major factors that influence the reliability and safety of Li-ion batteries. A general battery model considering both temperature and degradation is often difficult to develop, given the fact that there are many different types of cells with different shapes and/or internal chemical components. In response, a migration-based framework is proposed in this paper for battery modeling, in which the effects of temperature and aging are treated as uncertainties. An accurate model for a fresh cell is established first and then migrated to the degraded batteries through a Bayes Monte Carlo method. Experiments are carried out on both LiFePO4 batteries and Li(Ni1/3Co1/3Mn1/3) O-2 batteries under various ambient temperatures and aging levels. The results indicate that the typical voltage prediction error can be limited within +/- 20 mV, for the cases of temperature change up to 40 degrees C, and capacity degradation up to 20%. The proposed method paves ways to an effective battery management and energy control for electric vehicles or micro grid applications.