Abstract Deep convection from tropical cyclones (TCs) can reach the height of the tropopause and as such an interaction between the upper troposphere and lower stratosphere is likely to occur. Such interactions have been reported in both numerical and observational studies, mainly showing that subsidence from the stratosphere into the eye of an intensifying storm leads to a high‐level warm core. However, the effect of this upper‐level warming on the intensity of the TCs is not yet well understood. In this study, we show that subsiding air from the stratosphere beyond subsidence in the eye is the reason for the upper‐level warming in idealized simulations. We further show that it is possible to quantify the effects of the upper‐level warming on the potential intensity of the TC. Finally, we conclude that overshooting convection into the stratosphere causes the observed subsidence, as both become more pronounced with increasing sea‐surface temperatures (SST).