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We designed and have been fabricating a conduction-cooled 19 T superconducting magnet consisting of a NbTi coil, Nb3Sn coils and a Bi2223 insert coil. The insert coil is made up of 25 double-pancake coils, which are wound with the conductors composed of an Ag-sheathed Bi2223 tape and a stainless steel tape for reinforcement. The inner diameter and the outer diameter of each double-pancake coil are φ90 mm and φ180 mm, respectively. In order to investigate the mechanical and superconducting properties of the double-pancake coils, a model coil consisting of two double-pancake coils was fabricated and excited in liquid helium in the background fields up to 11 T and hoop stresses were applied to the model coil. It was found that the superconducting properties of the model coil did not change even after the hoop stress application of 52.7 MPa, which was exceeding the hoop stress applied in the 19 T superconducting magnet. The Bi2223 insert coil will be cooled by a GM-JT cryocooler to approximately 4.5 K through aluminum plates. Thermal stability analysis is very important especially for the conduction-cooled HTS coils operated at lower temperature since thermal runaway may cause the burnouts of the HTS coils. In this paper the analysis results are also discussed.