Adiabatic demagnetization refrigerator (ADR) attains cooling effect by exposing an alternating magnetic field to paramagnetic materials with significant magnetocaloric property. The temperature change and its subsequent cooling effect originates from the change of the magnetic entropy in the material under the influence of varying magnetic field. To achieve appreciable large cooling effect, high and fast varying magnetic field is required. Our group previously made the conduction-cooled HTS magnet, which stably produced magnetic field of 3.5 T with ramp rate of 0.23 T/s. The magnet, however, was permanently damaged at 4 T operation. The damaged HTS tape was located in the spot where the highest perpendicular field was generated by itself. It was speculated that the normal zone was formed very locally, and the detection system was not fast enough to detect quench before the large magnetic energy was dissipated in this zone. With the lessons from the previous magnet, a conduction-cooled HTS magnet was newly designed to produce AC magnetic field of maximum 4 T for an ADR. The HTS conductor with higher critical current density than that of the previous one is chosen to make the magnet in order to realize more safe operation. The magnet is to be made by short and thick solenoid shape and cooled by a commercial two-stage Gifford-McMahon cooler which provides 4 K environment. Electrical and thermal analysis are conducted to predict the critical current, the AC loss and the effect of thermal drains inserted between each layer of the magnet. Stress analysis is also conducted with the isotropic solenoid assumption. Detailed methods and results are presented and discussed.