We apply the 4C code, recently validated against different types of transients, to the simulation of the first stage of the cool-down of an ITER Toroidal Field (TF) magnet, from 300 K to 80 K. For a given scenario (inlet temperature, pressure and total mass flow rate evolution), we compute the evolution of the maximum temperature difference across the magnet. These results are compared both with the allowable and with the previously published results of another code, thus providing a benchmark for 4C. The differences between the models implemented in the two codes, whenever present, are highlighted, and their effects are analyzed by suitable sensitivity studies.