The Himalaya and Tibet are known for their huge granite batholiths that show geochemical signs of having formed by partial melting of the continental crust.  They also show signs of ductile zones in the deep crust.  Whether or not this ductility is associated with incipient melting cannot be judged easily, as there are no examples of active felsic volcanism.  However, it is possible to predict theoretically where crustal temperatures exceed the solidus of the crust, whose paths in pressure-temperature space for various amounts of water content is well known.  The problem is knowing the way in which temperature increases with depth.  That is usually estimated from the surface heat flow and modelling the likely thermal conductivity of different crustal layers, but it isn’t suitably precise.  German, US and Chinese geophysicists have tried a clever means of estimating crustal temperature using seismic data (Mechie, J. et al. 2004.  Precise temperature estimation in the Tibetan crust from seismic detection of the a-b quartz transition.  Geology, v. 32, p. 601-604).  Experiments show that quartz in its low-temperature a form transforms to b quartz above 575ºC at atmospheric pressure, and at higher temperatures with increasing pressure.  The P-T change in the transition is well known, so if b quartz can somehow be detected in the deep crust, its depth gives the crustal temperature.  As luck would have it, the transition results in a significant change in the elastic properties of quartz that should effect the speed at which seismic waves travel through rocks rich in b quartz.  More precisely, the P-wave speed should increase abruptly by a detectable amount.  Mechie and colleagues have indeed found the depth of this transition below a seismic profile running across part of the Tibetan Plateau NNW of Lhasa.  Its depth varies between about 20 to 15 km coinciding with the upper-middle crustal boundary.  At its shallowest levels, the transition is directly above a large zone of high electrical conductivity, discovered by magnetotelluric surveys, which has been suggested to be due either to a high content of aqueous fluids or crustal melts.  The geotherm (about 40ºC km^-1) associated with the shallow a-b quartz transition crosses the wet granite solidus about 5 km beneath it, so the lower crust itself is likely to be generating granitic magmas.  Although the deepest levels of the  a-b quartz transition also predict likely conditions for wet melting in the lower and middle crust, below those zones there is no evidence that it is happening.  One possibility is that water content varies considerably in the sub-Tibetan crust.  Where melts or fluids are moving in the crust, heat transfer is not purely by conduction, and steep geothermal gradients can stem from heat being transported upwards with moving fluids.