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The influence of the current slope (dI/dt) and thermal exchanges on the magneto-thermal transition of textured bulk YBCO are analyzed within the framework of the resistive Fault Current Limiter (FCL). This study was carried out at 90.5 K both in pressurized liquid nitrogen, in vacuum and when the YBCO sample is in contact with alumina plates. The superconductor U(I) response is governed by a power law, depends on dI/dt and is influenced by the thermal surroundings. These phenomena can be justified if the dissipated energy during the transition is concentrated in a small volume of the conductor. The second part of this paper deals with the thermal recovery of bulk materials. Even in the case of film boiling where the exchanges are poor, a thermal gradient due to the weak thermal conductivity of HTc materials appears in the section of the conductor. This point and its consequences are described and discussed by using a finite element software.