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This paper presents and analyzes test results in order to optimize the performance of a new-concept cryocooler-cooled HTS magnet, which is excited by a thermal electromotive force. This magnet system has the advantages of compactness, lightweight and continuous excitation in comparison with conventional HTS magnets. That is, a conventional HTS magnet is not suitable for operation in persistent-current mode, because an HTS coil has much larger flux flow resistance than an LTS coil. So, the magnet needs an external power source to maintain continuous magnetic fields. Accordingly, the concept of the HTS magnet excited by a thermal electromotive force of a thermoelectric element instead of an external power source was proposed. This magnet system will be simpler than a conventional one because it doesn't need the large external power source. Therefore, this magnet is suitable for applications in which there are severe constraints on the space and the weight. In a conventional magnet, a current lead connected to the HTS coil is designed to minimize the heat leakage to the coil. In the same way, for the new magnet system excited by thermal electromotive force, the optimum design of thermoelectric element is necessary to minimize the heat leakage. An experiment in which the HTS coil and the cold junction of the thermoelectric element are cooled by a cryocooler has been carried out. The heat leakage of our new magnet system using of Bi2Te3 thermoelectric elements was found to be 0.22 W/A by experiment. It is twice as high as that for optimized Cu current leads.