Galactic halos accrete material from the intergalactic medium (IGM) and part of this accretion is expected to be in the form of cool (T & SIM; 10(4) K) gas. A signature of this process could reside in the detection of numerous clouds in the circumgalactic medium (CGM). However, whether this material is able to accrete onto the galaxies and feed their star formation or, instead, evaporates into the CGM hot phase (corona, T & SIM; 10(6) K), is not yet understood. Here, we investigate the evolution of cool CGM clouds accreted from the IGM and falling through the hot corona of low-redshift disc galaxies, using 3D high-resolution hydrodynamical simulations. We include the effects of gravity due to the dark matter halo, isotropic thermal conduction, radiative cooling, and an ionizing UV background. We explored different values of parameters such as the halo mass, coronal mass, initial cloud velocity and strength of the thermal conduction. We find that the clouds lose the vast majority of their mass at distances larger than half of the galaxy virial radius and are completely dissolved in the corona before reaching the central galaxy. Resolving the Field length with at least 5-7 cells is crucial to correctly capture the evolution of the infalling cool gas. Our results indicate that cool IGM accretion can not feed star formation in z & SIM; 0 star-forming galaxies in halos with masses of 10(11.9) M-& ODOT; or above. This suggests that present-day massive star-forming galaxies can sustain their star formation only via the spontaneous or induced cooling of their hot corona.