We illustrate a quantitative conductive/convective thermal model incorporating a wide range of geophysical, petrological, geological, geochemical and isotopical observations that constrain the thermal evolution and present state of the Campi Flegrei caldera (CFc) magmatic system. The proposed model has been computed on the basis of the current knowledge of: (1) the volcanic and magmatic history of the volcano over the last 44 ka, (2) its underlying crustal structure, and (3) the physical properties of the erupted magmas. 3D numerical simulations of heat conduction and convection within heterogeneous rock/magma materials with evolving heat sources and boundary conditions that simulate magma rise from a deep (≥ 8 km depth) to shallow (2–6 km)...