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The active development of high temperature superconductor (HTS) materials has led to extensive research and development studies of superconducting transformers worldwide. Considerable benefits have been accomplished with the introduction of the HTS transformer such as reduced power loss, size, and transformer weight. However, recent advancement in the design technology has focused on the HTS transformer's ability to also perform as a fault current limiter (FCL). This paper presents the computation of the thermal effects of short circuit currents on a non-FCL HTS transformer and demonstrates how it will behave with an HTS-FCL winding conductor.