In the last years, the design of internal combustion engines (ICE) has evolved significantly, mainly because of the changing demand of mobility, the need to limit the pollution produced by vehicles, and recently, the opportunity to reduce emissions of climate-altering gases. Among the more interesting technologies, those connected to a revision of the engine cooling, as well as, in general, of the thermal needs on board vehicle (oil cooling, intercooling of the turbocharging air, EGR cooling, cabin conditioning...) appear very promising, also because characterized by a lower cost increase per unit of CO₂ saved. In this paper, the Authors present a mathematical model of an internal combustion engine physically consistent that appraises the performances of conventional and unconventional engine cooling systems and the integration of vehicle thermal needs. In particular, the Authors studied a double cooling circuit, at two different temperature levels, that allows several improvements in