The Advanced Photon Source Upgrade includes four 4.8-m long superconducting undulator (SCU) cryostats, each containing two up to 1.9-m long planar undulator NbTi magnets. The cooling is provided by six cryocoolers arranged in three thermal circuits. The magnets are indirectly cooled with LHe penetrating through channels in the magnet cores. This 4-K circuit which also includes a LHe tank, is cooled by five 4-K cryocooler 2nd stages. A beam vacuum that is thermally isolated from the magnets, is cooled by one 10-K cryocooler 2nd stage. A thermal shield and warm parts of current leads are cooled by the 1st stages of all six cryocoolers. This paper presents an ANSYS-based thermal analysis of the new SCU cryostat including all thermal circuits. The bench marked thermal conductance between the cryocooler cold heads and the LHe tank are used in the calculations as well as the measured cryocooler load lines. The model predicts temperatures in the system, total 4-K heat loads and an excess cooling power for various operational modes of the undulator.