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In order to stably and reliably remove the electromagnetic losses of the superconducting cavity through thermal conduction using cryocoolers, numerical simulations and experimental studies were conducted on the cooling structure and RF performance of the conduction-cooled superconducting cavity. Based on the geometric structure and electromagnetic losses of the 1.3 GHz superconducting cavity, various cooling structures were designed, and multiphysics simulation methods were employed to study the effects of the conduction cooling structure schemes, thermal conductive materials, and contact thermal resistance on the heat transfer capacity and superconducting cavity performance. Vertical tests were performed on the conduction-cooled 1.3 GHz Niobium and Nb3Sn superconducting cavities using a cryostat without liquid helium. The test results indicate that the optimized cooling structure has good heat transfer performance, with a slow cooling rate of 0.035 K/min (from 22 K to 7 K) and an average temperature difference across the cavity of 0.2 K. The highest accelerating gradient achieved in the 1.3 GHz Niobium cavity tests was 4.45 MV/m at 6.2E8, with the temperature at the equator being approximately 4.4 K; subsequent temperature increases led to a continuous decrease in Eacc and Q0. The maximum accelerating gradient obtained in the Nb3Sn superconducting cavity tests was 4.4 MV/m at 3E9, with the equatorial temperature around 3.8 K. The research results presented in this paper provide valuable reference for improving the RF performance of conduction-cooled superconducting cavities and designing conduction-cooled superconducting modules.