During heat waves, the capacity and demand for cooling shelters can change depending on the temperature-humidity index. In this presentation, we explore the application of the temperature-humidity index to estimate both the capacity and demand for cooling shelters. Using these estimates, we propose a bi-objective integer linear programming model to allocate heat-vulnerable residents to cooling shelters. Our model is validated with a case study in Ulsan Metropolitan City, South Korea. We prioritize heat-vulnerable residents based on the temperature-humidity index, and assign them to cooling shelters with the objectives of maximizing coverage and minimizing the total operating cost. Our approach can improve the efficiency and effectiveness of cooling shelter allocation during heat waves.