We employ 2-D thermo-mechanical modelling to study possible mechanisms for generating large-scale crustal magmas in the Altiplano–Puna region of the Central Andes. The peak of ignimbrite activity in the late Miocene and Pliocene is associated in space and time with tectonic shortening and plateau uplift. A seismic low-velocity zone and other geophysical observations indicate that partial melting in the mid-crust is still present under the ignimbrite province today. We show that neither radiogenic heat production in a thickening crust, nor shear heating due to tectonic shortening, nor heat brought by intrusions of arc magmas into the mid-crust can heat the mid-crust to the degree and within the time frame suggested by the geologic, petrologic and geophysical observations. A viable mechanism to achieve high temperatures within the time constraints is convective heat and mass transfer by partially molten lower crust which itself was heated by enhanced mantle heat flow, possibly associated with delamination of the mantle lithosphere during tectonic shortening and intensified magmatic arc activity. The thermo-mechanical models explain the mid-crustal low-velocity zone and the high and strongly variable surface heat flow observed in the Altiplano. Convection by bulk flow of the crust appears when the middle and lower crust are mechanically weak (quartz-dominated rheology), the basal heat flow from the mantle is high (>60 mW/m²) and tectonic shortening is active. We argue that these conditions are satisfied in the Central Andes orogen.