In extreme high-temperature conditions, rapid changes in electricity demand, coupled with a decline in primary energy generation capacity, lead to a significant reduction in both power supply capacity and energy reserve. To address the issue of dual shortages in power and energy when there is extreme heat, an optimization study of day-ahead load management in an urban power grid is conducted. First, considering the sharp increase in residential air conditioning load during extreme heat, an incentive-based demand response strategy is adopted to encourage residents to reduce air conditioning power consumption. Considering the variations in comfort requirements among different residents, the adjustable potential of residential air conditioning load is analyzed. Next, the impact of different load management measures on power and energy shortages is analyzed, and a load management model for an urban power grid in extreme heat conditions is established from both economic and administrative management perspectives. Then, to account for the demand response uncertainty while coordinating grid reconfiguration with mobile energy storage deployment measures, a two-stage robust optimization model is constructed to minimize the impact on residential load losses and industrial-commercial economic losses. A strategy for optimizing day-ahead load management in an urban power grid to address dual power and energy shortages is formulated. Finally, the effectiveness and feasibility of the proposed optimization model are verified by numerical simulation.