Load forecasting is critical for effective scheduling and operation of power systems, which are becoming increasingly complex and uncertain, especially with the penetration of distributed power. This paper proposes a data-driven deep learning framework to forecast the short-term power load. First, the load data is processed by Box-Cox transformation. The tail-dependence of the power load on electricity price and temperature is then investigated by fitting the parametric Copula models and computing the threshold of peak load. Next, a deep belief network is built to forecast the hourly load of the power system. One-year grid load data collected from urban areas in both Texas and Arkansas, in the United States, is utilized in the case studies on short-term load forecasting (day-ahead and week-ahead) is conducted for four seasons independently. The proposed framework is compared with classical neural networks, support vector regression machine, extreme learning machine, and classical deep belief networks. The load forecasting performance is evaluated using mean absolute percentage error, root mean square error, and hit rate. The proposed framework outperforms the tested state-of-the-art algorithms, with respect to the accuracies of both day-ahead and week-ahead forecasting. Overall, the computational results confirm the effectiveness of the proposed data-driven deep learning framework.