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Urban cooling demand (UCD) is shaped by various aspects of urban morphology, and systematically quantifying these correlations is essential for mitigating heat stress amid ongoing urbanization and climate change. When implementing national-scale mitigation strategies or addressing rising cooling demands, the variability in urban form across cities within similar climatic zones leads to disproportionate cooling needs at regional scales, rendering generalized approaches ineffective. Therefore, an integrated top-down approach that accounts for urbanization variability to predict or benchmark UCD would be more beneficial for stakeholders from individual building to city level. This study categorizes rapidly urbanizing Indian cities into four types based on ten key features of urban built development---horizontal expansion, vertical growth, volumetric densification, and population growth---and their impact on city-wide cooling needs over distances of 50 to 100 km. Type-I cities are large, high-density, and irregularly shaped; type-II cities are medium-sized with similar characteristics; type-III cities are small with moderate density; and type-IV cities are compact and low-density. Key findings reveal a strong correlation between vertical development and UCD, with coefficients of 0.91 and 0.83 for different percentile ranges. UCD measure (i.e., expressed in terms of the yearly mean of cooling degree days) ranges from 7.0 to 10.0 °C-Year in type-I cities and 8.5 to 11.0 °C-Year in type-II cities, while type-III cities show a broader range of 4.0 to 10.0 °C-Year and type-IV cities a narrower range of 9.0 to 10.0 °C-Year. Multi-linear regression analysis indicates that while individual C-BU features exhibit limited predictive power (R2 = 0.745), combining similar typologies enhances model robustness.