Extreme temperatures can push various power grid components to their operational limits. To make matters worse, the available capacity of most assets gets negatively affected as the temperature increases beyond certain thresholds. Unsurprisingly, this temperature-induced reduction in available power generation and transmission capacities coincides with higher electric demand on the system, mostly attributed to the over-utilization of air-conditioning (A/C) systems. This can jeopardize the ability of the power grid to effectively maintain the balance between load and generation. Incorporating temperature into the dispatch model of the grid is not only critical for the reliability and security of the grid operation, but also helps avoid overloading assets, which could otherwise lead to loss of life and premature failure. A unified framework is proposed in this paper to optimally allocate available energy and demand responsive resources in a power distribution system exposed to a heat wave event in order to simultaneously maintain load-generation balance and minimize operational cost. To regulate demand, the proposed solution generates temperature set-points for individual demand responsive A/C units. However, it utilizes this resource conservatively in order to avoid health risks to the residents, particularly children and the elderly. Due to the multi-objective nature of the problem, a goal programming approach is adopted to ensure the Pareto optimality of the final solution.