In developing cities, rapid urbanization and climate change leads to drought and urban heat island effects which affects the energy consumption, economy and the environment. Extreme temperature rise has amplified the stress on vulnerable groups and has reduced livability. The sustainability of a city lies in the adaptability of the city to the climatic stresses. The role of adaptability is guided by the contextual vulnerability assessment of the city. This paper intends to assess the contextual vulnerability of Madurai, an ancient city with high social and cultural value. Composite heat vulnerability index (CHVI), a function of exposure, sensitivity and adaptive capacity of the context has been construed by many as the quantitative representation of the vulnerability of a place to high temperature. This paper focuses on the development of a framework to assess the CHVI considering the contextual socio-cultural indicators like social capital and cultural value along with components of meteorological, geophysical, biophysical, fragility, socially-marginalised, and development quotient .The research methodology identifies suitable context specific indicators, computes and maps exposure, sensitivity and adaptive capacity indices, spatially maps the categorised vulnerable zones and identifies the critical indicators that contribute to vulnerability. The framework can support decision-making to enable socially resilient cities.