As the frequency, duration, and intensity of heat waves have been increasing in recent decades, the effective and efficient allocation of cooling shelters has become a significant issue in many cities. This study presents an integer programming model for allocating cooling shelters with the two conflicting objectives of maximizing coverage for the heat-vulnerable population and minimizing total operating cost of the cooling shelters. The temperature-humidity index is included in the model to reflect the weather conditions that affect heat waves. We also introduce data analysis procedures using real-time floating population data so as to track the hourly number and locations of individuals in the heat-vulnerable population. The proposed model is then validated with an application to Ulsan Metropolitan City in the Republic of Korea in which heat-vulnerable people are assigned to existing and potential cooling shelters. Given the condition of restricted budgets, we categorize and prioritize heat-vulnerable people into several groups using a clustering method and heat vulnerability index, and we suggest effective policy recommendations, so the most vulnerable people are provided cooling services first. In addition, we perform a sensitivity analysis on weather conditions, travel distance, electricity cost, and percentage of heat-vulnerable population served by cooling shelters, so policy makers can be prepared to respond quickly to the various factors that can change during a heat wave and ultimately reduce heat-related morbidity and mortality.