Aiming at the traffic surge problem caused by massive smart device access in Power Internet of Things(PIoT), a resource scheduling strategy of Mobile Edge Computing(MEC) with delay and energy consumption equalization is proposed. Considering the channel conditions, the safety temperature protection mechanism of electric equipment and the energy consumption of equipment, the energy consumption model and thermal power consumption constraints on the equipment side are constructed based on the Landaer principle. Under the premise of ensuring queue stability, the long-term average time energy consumption of the system is minimized by jointly optimizing the task offloading decision, transmission power and computational resource allocation. To solve this stochastic optimization problem, Lyapunov theory is introduced to transform the problem into a deterministic optimization problem for each time slot. Simulation results show that this strategy is able to reduce the system energy consumption relative to the baseline scheme and achieve an equilibrium between energy consumption and delay.