A thermal modeling of the Vesuvius is presented, based on its magmatic and volcanic history. A 2D numerical scheme has been developed to evaluate the heat transfer inside and around a magma body, the latent heat of crystallization and the inputs of magma from the asthenosphere to a crustal reservoir. Assuming a ratio >1 between velocities of magma ascending in the conduit and magma laterally displaced in the reservoir, the results indicate that, after 40 ka, the reservoir is vertically thermally zoned. As a consequence it hosts magma batches that can individually differentiate, mix and be contaminated by the crust, and produce the spectrum of isotopic compositions of the Vesuvian products. The thermal model reproduces the geothermal gradient and the brittle-ductile transition (250--300¿C) at 6 km of depth (the maximum depth of earthquake foci) only after 0.5--1 Ma, implying a long lived magma chamber below the volcano.