The Tibetan plateau, like any landmass, emits energy into the atmosphere in the form of dry heat and water vapour, but its mean surface elevation is more than 5 km above sea level. This elevation is widely held to cause the plateau to serve as a heat source that drives the South Asian summer monsoon, potentially coupling uplift of the plateau to climate changes on geologic timescales. Observations of the present climate, however, do not clearly establish the Tibetan plateau as the dominant thermal forcing in the region: peak upper-tropospheric temperatures during boreal summer are located over continental India, south of the plateau. Here we show that, although Tibetan plateau heating locally enhances rainfall along its southern edge in an atmospheric model, the large-scale South Asian summer monsoon circulation is otherwise unaffected by removal of the plateau, provided that the narrow orography of the Himalayas and adjacent mountain ranges is preserved. Additional observational and model results suggest that these mountains produce a strong monsoon by insulating warm, moist air over continental India from the cold and dry extratropics. These results call for both a reinterpretation of how South Asian climate may have responded to orographic uplift, and a re-evaluation of how this climate may respond to modified land surface and radiative forcings in coming decades.