In this work, the temperature dependence of the resistive switching-related currents (gate and drain) in MOSFETs with ultra-thin Hf based high-k dielectric has been analyzed, for the two dielectric conductivity states. The two different conductive states of the resistive switching have been associated to the breakdown (BD) and BD recovery of the dielectric. The results about the temperature dependence of the post-BD gate current are in agreement with those obtained from the study of the injected charge to recovery, a useful parameter to analyze the switch from the high to the low conductivity state. The drain current in the MOSFETs, for the two conductivity states, for different locations of the BD path along the channel (source and drain) and several temperatures has also been studied. The results are a contribution for a better understanding of the resistive switching phenomenon in ultra-thin gate dielectrics, which could be useful for the developing of models to describe BD reversibility.