YBCO(YBa2Cu3O7) wires have superior characteristics such as high energy densities, thus allowing the fabrication of large-scale, high power-output superconducting equipment applications. A high voltage is desired to achieve a large power output from a superconducting coil, and is realized by improving the insulating properties of the coil with the introduction of solid insulation. However, because high temperature superconducting wires have high critical temperatures and thermal tolerance compared to metal-based superconducting wires, the benefits offered allow the insulated superconducting coil to be directly cryocooled. In a helium circulation cryocooling system, the aluminum-fabricated transmission heat shields are coated around the surface of the coils to cryocool equally, and are embedded into the transmission heat shields with the conducting pipe allowing helium gas to circulate. We manufactured a conduction cooled model coil of 600 mm class diameter, and have verified the ability to realize a cooling of more than 3 W/m2 for coil surface heat flux at an operating temperature of 20 K using the demonstration cooling system. In addition, we have also evaluated the electric insulation performance, which is in contradiction to the cooling performance. The conduction-cooled YBCO coil withstood up to DC 13 kV voltages at 20 K.