A two-dimensional calculation code of He II heat conduction, using implicit method, has been developed. It considers a heat conduction equation of He II, omitting some parameters of the two-fluid model. Implicit method can avoid numerical instabilty from a mutual friction term. The computation time and computer power for the calculation can be saved. The temperature distribution of He II for various heat inputs, bath temperatures, and heater lengths may be calculated on a personal computer in short time.