The available power of vehicle-mounted batteries needs to be real-time predicted to accommodate prospective driving demands of overtaking, gradient climbing, constant-speed cruising, and regenerative braking. Generally, battery power capabilities are limited by multiple constraints, for example, terminal voltage, current, state-of-charge (SoC), and State-of-Energy (SoE). This paper constructs SoC and SoE estimators resorting to the square-root central difference Kalman filter (SR-CDKF) and an equivalent circuit model with online updated parameters. In addition, a battery thermal evolution model is formulated, whereby the ordinarily ignored temperature constraint is taken into account. Based on above achievements, a battery power prediction scheme conforming to multiple constraints is realized. Finally, experimental verifications are conducted on a LiFePO4 battery pack subject to consecutive Federal Urban Driving Schedule profiles. The SR-CDKF-based SoC and SoE estimators give accurate results under different conditions. In contrast to the conventional PNGV-HPPC method, the proposed method behaves with more reliability and robustness at different time horizons, temperatures, and aging levels. The assessment results justify the effectiveness of the battery modeling and algorithm utilization efforts.