The seasonal evolution of the Asian summer monsoon (ASM) is closely related to the reversal of the meridional temperature gradient between the Tibetan Plateau (TP) and the adjacent ocean in the upper troposphere. Sensible heating has been suggested to play a crucial role in tropospheric warming over the TP. More recently, adiabatic subsidence associated with the Matsuno‐Gill type atmospheric response was shown to warm the upper troposphere downward from the tropopause around the TP at the onset phase of the ASM. Here, we suggest the crucial role of convective heating in the seasonal evolution of the ASM, focusing on the seasonal march of the monsoon trough and seasonal upper‐level warming around the TP. Correlation analyses and numerical experiments showed that convective heating around the Maritime Continent, which induces upper tropospheric warming over the southern slope of the TP together with southward extension of the monsoon trough around the Bay of Bengal forming the twin‐cyclone structure, is indispensable to the Southeast Asian summer monsoon onset. Meanwhile, convective heating around the Bay of Bengal, which induces upper tropospheric warming to the southwest of the TP together with westward extension of the monsoon trough from the Bay of Bengal to the Arabian Sea, is necessary for the Indian summer monsoon onset. Thus, although the TP has been emphasized previously, convective heating is a necessary factor in explaining the seasonal upper‐level warming around the TP and the seasonal march of the ASM.