Abstract: A pair of interaction region superconducting quadrupole (SCQ) magnets in Beijing Electron-Positron Collider Upgrade (BEPCⅡ) are key facilities cooled by liquid helium in the constrained cooling channels. The heat loads to the SCQ magnet and temperature contour of the magnet cryostat are calculated. Based on the calculation, the method to decrease the heat load is presented. The results of thermal fluid modeling for the magnet cryostat are also provided. Two types of cooling schemes, the subcooled liquid helium and the supercritical helium flow, are numerically analyzed.