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From the viewpoint of a cryogen-free high-field superconducting magnet, the thermal stability properties of YBa2Cu3O7 (Y123) coated conductor tapes before thermal runaway are examined under the conduction-cooling condition by a GM-cryocooler. Under such cryocooling condition, Ag-sheathed Bi2Sr2CaCu2O8 (Bi2212) wires with Jc ~ 104 A/cm2 reveal stable behaviors of 3 times larger current properties before thermal runaway than critical currents, although conventional Nb3Sn wires with Jc ~ 104 A/cm2 quench almost at their critical currents under the cryocooling condition. In order to determine the maximum current-carrying capacity of the Y123 tape in high fields, we use a zero-dimensional heat balance model. On the basis of the measured basic properties for the Y123 tape, the calculations were done at B=20 T, bath temperature T0=4.2 K, Jc ~ 107 A/cm2, and cryocooling heat transfer coefficient h=10-3 W/cm2K. We found that the Y123 tape with Jc ~ 107 A/cm2 does not have the over-critical current but rather the sub-critical current before thermal runaway.