Sections of the superconducting magnets of the SIS100 particle accelerator, under construction at the Facility for Antiproton and Ion Research (FAIR), the Society for Heavy Ion Research (GSI), Darmstadt, are going to be connected with the by-pass lines. Each line will be used to transfer a two-phase helium flow and an electric current. The electric current will be carried by four pairs of superconducting Nuclotron-type cables. Fast-ramping currents are expected to cause the generation of heat within the cables. In this work the results of a numerical thermal analysis of a bus-bar are presented. The amount of heat transferred from the environment was found based on geometric dimensions of the line and applied insulation. The amount of hysteresis loss, generated in the cable during the operation under most demanding regime of the operation of the accelerator, was calculated. According to the amount of the generated heat, the amount of the hysteresis loss is low in relation to the heat generated in the superconducting magnets. Also it was found that the cable used in the line still retains a large margin of current-carrying capacity.