Despite experiencing hot weathers, limited studies from India explored relationships between ambient heat and health. We studied associations between heat and all-cause mortality to estimate heat threshold(s) affecting health, and examine other affecting dimensions. We conducted time-series analysis with daily maximum temperature and all-cause mortality data of Bhubaneswar city (March-July, 2007-2017), and explored their interactions. Mortality risks rose when daily maximum temperatures were >36.2 degrees C (lower threshold), and even more when >40.5 degrees C (upper threshold). Every degree above36.2 degrees C increased the mortality risk by 2% (mortality rate ratio: 1.02; 95% CI 1.01, 1.03). The effects of maximum temperature increased on days when minimum temperatures were >25.6 degrees C (median). The effect of heat was immediate and lasted for 0-1 day with no lagged effect. Two temperature thresholds with varying mortality risks provided an opportunity for a graded heat warning system. The accentuation of the deleterious effects of heat by the higher minimum temperature calls for its inclusion in the heat warning system in future.