Intensifying urban heat significantly exacerbates existing disparities in exposure and coping capacities, creating an urgent need for equity-focused adaptation strategies. Since traditional resilience planning is often fragmented, this paper suggests that an Urban Digital Twin (UDT) is essential for integrating these resilience planning components into a cohesive system. This conceptual paper proposes a reusable UDT framework specifically designed to enhance climate resilience by testing scenarios in three core areas: physical infrastructure, social dynamics, and institutional governance. To achieve this, the study proposes a minimum UDT architecture comprising the following structure: an environmental module, a social vulnerability module, and a decision-making module. This operational design allows for the testing of three distinct scenario categories: (1) physical interventions in the built environment, (2) social support mechanisms for at-risk populations, and (3) institutional strategies for policy implementation. Most existing standard approaches rely on temperature and environmental analysis, whereas this multidimensional methodology argues for the distributional equity of interventions. This paper suggests that integrating these three main components within a UDT environment is critical for decision-makers. It enables the identification of strategies that effectively protect the most vulnerable residents, rather than merely optimizing for city-wide temperature averages, ultimately fostering more just urban climate governance to ensure lasting social equity and systemic resilience.