A hybrid CFD/integral approach is used to predict the noise spectrum of a real automotive fan cooling system. The tonal and broadband noise spectral components, mainly due to the coherent and random part, respectively, of the unsteady pressure fluctuations induced by the rotor-wake/stator-vane interaction, are computed by applying a Ffowcs-Williams & Hawkings acoustic analogy to the wall pressure field provided by a transient Reynolds-averaged Navier-Stokes simulation, with superimposed random fluctuations computed through a stochastic method. The RANS turbulent quantities are used to generate solenoidal stochastic velocity fluctuations that contribute to define the right-hand side of a Poisson equation for the pressure perturbation. The Poisson equation is cast into a boundary integral equation and solved by means of a boundary element method. The noise spectra at different angles with respect to the fan axis are computed and compared with available experimental data.