This paper discusses the fabrication of a (RE)BCO solenoid magnet and its experimental results from the aspect of AC loss and thermal characteristics. A (RE)BCO coated conductor with polyimide tape insulation was utilized for a coil and wound by a standard layer-wound method. The (RE)BCO solenoid magnet consists of a stainless steel bore and a pair of OFHC copper supporting plates assembled at both ends. The coil winding has a novel thermal drain structure that can withstand high AC thermal loads generated externally and internally. The OFHC copper strips were installed between the interlayers in the perpendicular direction to the (RE)BCO conductor winding to mitigate both thermal resistance in the axial direction of the (RE)BCO coil and eddy current loss by an external magnetic field. Apiezon (R) N grease with hexane solution was applied on the entire (RE)BCO coil winding to minimize thermal contact resistance between the conductor and the OFHC copper strips. The (RE)BCO coil carried 150 A at 14.7 K and generated 3.5 T at the center of the coil. A sinusoidal current waveform (operating frequency from 0.1 Hz to 1.0 Hz) was applied with peaks of 25 A, 50 A, and 70 A (the corresponding magnetic field of 0.54 T, 1.08 T, and 1.54 T) and the corresponding AC losses were measured by both calorimetric and electrical methods. The AC losses measured by both methods were in good agreement. The experimental results were compared with theoretical and numerical solutions.