Using a 13-year dataset of Atmospheric Infrared Sounder (AIRS) retrieved temperature profiles including 5019 AIRS overpasses in 1061 tropical storm through category-2 tropical cyclones (TCs) in global basins during 2002–2014, this study examines the relationship between the warm-core structure and TC intensity change with a focus on rapid intensification (RI). The AIRS TC overpasses are classified into RI, slowly intensifying (SI), neutral (N), and weakening (W) categories. The effect of the warm-core structure upon TC intensification is entangled with that upon TC intensity. It is necessary to exclude the weakening category in order to single out the relationship between TC intensification and warm-core structure from a statistical method. The composite warm-core maximum temperature anomaly is the strongest in RI storms (~7 K), followed by W (~6 K), SI (~5 K) and N (~ 4 K) storms. RI storms have the highest equivalent potential temperature ( θ e ) and CAPE in the eye among all intensity change categories. The warm-core structure of RI storms is asymmetric relative to shear, with the higher temperature anomaly and convective available potential energy (CAPE) located in the down-shear quadrant. When only considering samples with intensification rates ≥0, a significant and positive correlation is found between the warm-core strength and TC intensification rate. The warm-core height is also positively correlated with the TC intensification rate at a high confidence level. The AIRS-derived warm-core temperature anomaly greater than 4 K and weighted warm-core height higher than 450 hPa are the necessary conditions for RI. • Warm-core strength is positively correlated with TC intensification rate. • Warm-core height is positively correlated with TC intensification rate. • RI never happens when warm-core temperature anomaly less than 4 K. • RI never happens when weighted warm-core height lower than 450 hPa.