Longwave cloud feedback is systematically positive and nearly the same magnitude across all global climate models used in the Intergovernmental Panel on Climate Change Fourth Assessment Report (AR4). Here it is shown that this robust positive longwave cloud feedback is caused in large part by the tendency for tropical high clouds to rise in such a way as to remain at nearly the same temperature as the climate warms. Furthermore, it is shown that such a cloud response to a warming climate is consistent with well-known physics, specifically the requirement that, in equilibrium, tropospheric heating by convection can only be large in the altitude range where radiative cooling is efficient, following the fixed anvil temperature hypothesis of Hartmann and Larson (2002). Longwave cloud feedback computed assuming that high-cloud temperature follows upper tropospheric convergence-weighted temperature, which we refer to as proportionately higher anvil temperature, gives an excellent prediction of the longwave cloud feedback in the AR4 models. The ensemble-mean feedback of 0.5 W m−2 K−1 is much larger than that calculated assuming clouds remain at fixed pressure, highlighting the large contribution from rising cloud tops to the robustly positive feedback. An important result of this study is that the convergence profile computed from clear-sky energy and mass balance warms slightly as the climate warms, in proportion to the increase in stability, which results in a longwave cloud feedback that is slightly smaller than that calculated assuming clouds remain at fixed temperature.