Accurate estimation of the state of charge (SOC) and state of health (SOH) is critical for ensuring the safety and reliability of lithium-ion batteries, especially under varying temperature conditions. Temperature significantly impacts battery performance, introducing non-linear effects that complicate state estimation. This paper proposes a novel multi-scale co-estimation strategy that integrates a temperature-dependent fractional-order model (FOM) with a dual fractional-order adaptive unscented Kalman filter (DFOAUKF). The FOM is developed based on electrochemical impedance spectroscopy and the temperature-dependent open-circuit voltage, capturing intrinsic electrochemical characteristics of the battery. Parameters are identified using a combined offline and online method. The DFOAUKF algorithm leverages the time-scale differences between SOC and SOH, enabling micro-time SOC estimation in seconds and macro-time SOH estimation over test cycles, while adaptively updating noise covariance matrices. Experimental validation under dynamic stress test (DST) and urban dynamometer driving schedule conditions at 10