Large variations of the heat load coming from the superconducting magnets to the cryoplant in a tokamak are an undesired consequence of the intrinsically pulsed operation of the machine. In this paper, the cryogenic circuit module of the 4C (Cryogenic Circuit Conductor and Coil) code is used to analyze a subset of the results on pulsed load driven transients experimentally simulated in 2011 in the HELIOS facility (HElium Loop for hIgh lOads Smoothing) at CEA Grenoble, France. We focus on the tests where the smoothing of the pulsed heat load from the supercritical helium loop to the saturated helium bath was achieved by means of a controlled bypass valve. To address this issue, the modeling capability of the cryogenic circuit module of the 4C code is extended to include PI controllers. The computed evolution of temperature, pressure and mass flow rate at different circuit locations shows a good agreement with the measurements, both in the SHe loop and in the LHe bath. These results confirm the accuracy of 4C and contribute a needed step in the process of validation of the code.