We investigated the time evolution of heat waves and warm nights over the 7 agroclimatic zones of Tamil Nadu, India, during the period 1951-2016, including the spatiotemporal patterns of concurrent hot day and hot night (CHDHN) episodes and the concurrent warm spells in daytime temperature and drought (CWD) episodes. The research relied upon gridded temperature and rainfall observations from the India Meteorological Department. We used the Heat-Wave Magnitude Index daily to study the warm spells in daytime and nighttime temperature, while the analysis of droughts was based on the Standardized Precipitation Evapotranspiration Index. We observed a considerable increase in the count, intensity and duration of heat waves and warm night episodes across Tamil Nadu between the periods 1951-1983 and 1984-2016. Particularly, the number of heat wave events almost doubled in the second half of the study period. We observed a west-east gradient in the severity of heat waves. The intensity and duration of warm night events increased up to 3-fold in the second half of the study period, especially over central Tamil Nadu. The study recorded a multi-fold increase in the number and frequency of CHDHN episodes and the number of CWD episodes during 1984-2016 compared to the base period 1951-1983. More importantly, the incidence of compound events that coexisted with anomalous phases of sea surface temperatures registered a statistically significant spike in many locations. These changes in temperature-induced extremes pose an exceptional public health threat that can increase morbidity and mortality, disproportionately affecting vulnerable sections of Tamil Nadu's populace engaged in outdoor work.