We present an integrated spatio-temporal framework for multi-range traction power and speed prediction for connected vehicles (CVs). It combines data-driven and model-based strategies to enable CVs energy efficiency optimization. The proposed framework focuses on urban arterial corridors with signalized intersections, and leverages the historical and real-time data collected from CVs and infrastructure to predict location-specific traction loads (e.g. acceleration at intersections), and augment them with time-specific speed profiles (e.g., stop duration at intersections). A Bayesian network is developed to provide a long-term load prediction informed by probabilistic analysis of historical traffic data at intersections and between intersections. Moreover, a shockwave profile model is adopted for modeling the queuing process at intersections by leveraging vehicle-to-infrastructure (V2I) communications, providing a short-range prediction of the vehicle speed with an enhanced accuracy. The benefits of the proposed load prediction framework are demonstrated for energy management of connected hybrid electric vehicles (C-HEVs). By incorporating the predicted loads into a multi-horizon model predictive controller (MPC), integrated power and thermal management of light-duty C-HEVs is enabled over real-world driving cycles, demonstrating a near globally-optimal fuel consumption over the entire trip with a < 1% deviation from dynamic programming (DP) results.