Driven by explosive computation demands of Internet of Things (IoT), mobile edge computing (MEC) provides a promising technique to enhance the computation capability for mobile users. In this paper, we propose a joint resource allocation and load management mechanism in an MEC system with wireless power transfer (WPT), by jointly optimizing the transmit power for WPT, the local/edge computing load, the offloading time, and the frequencies of the central processing units (CPUs) at the access point (AP) and the users. To achieve an energy-efficient and sustainable WPT-MEC system, we minimize the total energy consumption of the AP, while meeting computation latency requirements. Cooling energy which is non-negligible, is taken into account in minimizing the energy consumption of the MEC system. By rigorously orchestrating the state-of-the-art optimization techniques, we design an iterative algorithm and obtain the optimal solution in a semi-closed form. Based on the solution, interesting properties and insights are summarized. Extensive numerical tests show that the proposed algorithm can save up to 90.4% the energy of existing benchmarks.