The novel type of cable under consideration is cooled by gaseous Helium at elevated pressure. Helium is known for having poor electric breakdown strength; therefore the dielectric capabilities of this type of cable must be tested under conditions similar to the envisaged operation. In order to study the dielectric performance we have designed and built a novel high pressure cryostat rated at 2.17 MPa which has been used for testing model cables of lengths of up to 1 m. The cryostat is an open system where the gas is not re-circulated. This allows maintaining a high purity of the gas. The target temperature range is between 40 K and 70 K. This substantially increases the critical current density of the HTS compared to 77 K, which is the typical temperature of cables cooled by liquid nitrogen. The cryostat presented allows for adjusting the temperature and keeping it constant for the time necessary to run a complete dielectric characterization test. We give a detailed description of the cryostat. Measurements of partial discharge inception voltages as well as the temperature distribution along the model cables as a function of time are presented.