This study examines the vertical structures of temperature and convection associated with rapid intensification of tropical cyclones using collocated Advanced Microwave Sounding Unit (AMSU) and HURSAT‐B1 satellite observations for 2003–2015. We used AMSU measurements from six satellites: AQUA, MetOp, NOAA‐15, NOAA‐16, NOAA‐17, and NOAA‐18. Eighteen thousand three hundred sixty nine collocated satellite overpasses of tropical cyclones were obtained. Vertical structures of temperature and convection are analyzed for different categories of tropical cyclone intensity, for the composite lifecycles of tropical cyclones in different ocean basins, and for the rapid intensification events. Tropical cyclones reaching hurricane intensity are generally associated with warm core above eyewall cloud top extending into the stratosphere, suggesting the existence of warm stratospheric downdrafts penetrating into the central eye. Rapid intensification of tropical cyclones are generally associated with strong warming rate above eyewall cloud top that extends into the stratosphere, suggesting that stratospheric downdrafts are involved in rapid intensification of tropical cyclones.