A conduction-cooled high temperature super-conducting (HTS) solenoid is fabricated to produce pulsat-ing 4 T magnetic field for magnetic refrigeration. HTS con-ductor of 245 m is wound as a solenoid with 112 layers each of which consists of 12 turns of the conductor. For a stable ramping operation of the magnet, AC loss inside the wind-ing pack should be effectively rejected to the heat sink. The thermal drains are inserted between the layers and con-nected to the magnet flange which is cooled by a commercial two-stage Gifford-McMahon cooler. They are made of Ox-ygen-Free High Conductivity (OFHC) copper, and has a width of 6 mm and a thickness of 50 μm. Thermal analysis is conducted to confirm the effect of the thermal drain on the AC loss heat rejection. AC loss of the magnet is esti-mated by using T-A formulation (current vector potential T and magnetic vector potential A). The ramp rate of the mag-net and the heat sink temperature are set to 0.1 T/s and 4.5 K, respectively. In the thermal diffusion calculation, each winding layer is considered as the lumped capacitance. In addition, thermal conduction between the adjacent lay-ers and that through the thermal drains are considered. The thermal analysis confirms that the conductor temperature of the winding is maintained lower than the operating limit of 20 K. Based on the results of the thermal analysis, the stable pulsating operation of the conduction-cooled super-conducting magnet is predicted to be feasible and is also confirmed by the experiment.