The high temperature superconducting (HTS) solenoid magnet is preliminarily tested before constructing the adiabatic demagnetization refrigerator (ADR). The constructed magnet needs to operate in an AC mode to produce the maximum center field of 4 T with 0.1 T/s ramp rate. A commercial two-stage Gifford-McMahon (G-M) cooler is utilized as the heat sink for the conduction-cooling of the constructed magnet. The experiment shows that the magnet has a magnet constant of 20.4 mT/A at the center field. The resistive voltages in the conductor are extracted by eliminating the inductive voltage, and the current is to be dissipated in the dump resistor when the voltages of the conductor exceed the quench criteria (0.1 μV/cm). The 4 T experiment is conducted by producing the current of 200 A with 5 A/s ramp rate to the magnet. During the five cycles of the AC operation, the monitored resistive voltages did not violate the quench criteria. However, the continuous temperature rise at one of the current leads was observed, thus, the test was terminated before reaching the cyclic steady state. It is speculated that the joule heating at the joint of the current lead caused the temperature rise. The detailed experimental results are presented and discussed.