Cryosurgery is a rapidly developing discipline, alternative to conventional surgical techniques, used to destroy cancer cells by the action of low temperatures. Currently, the refrigeration is obtained via the adiabatic expansion of gases in probes used for surgeries, with the need of inherently dangerous pressurized vessels. The proposed innovative prototypal apparatus aims to reach the cryosurgical temperatures exploiting a closed-loop refrigeration system, avoiding the hazardous presence of pressurized vessels in the operating room. This study preliminarily examines the technical feasibility of the cryoablation with this machine focusing the attention on the cryoprobe design. Cryoprobe geometry and materials are assessed and the related heat transfer taking place during the cryoablation process is simulated with the aid of the computational fluid dynamics software ANSYS®Fluent. Parametric analyses are carried out varying the length of the collecting tubes and the inlet velocity of the cold carrier fluid in the cryoprobe. The values obtained for physical quantities such as the temperature reached in the treated tissue, the width of the obtained cold front, and the maximum pressure required for the cold carrier fluid are calculated and discussed in order to prove the effectiveness of the experimental apparatus and develop the machine further.