Reciprocity relations between ordinary temperature and the Frieden-Soffer Fisher temperature

Frieden and Soffer conjectured some years ago [Phys. Rev. E 52, 2274 (1995)] the existence of a "Fisher temperature" T-F that would play, with regards to Fisher's information measure I, the same role that the ordinary temperature T plays in relation to Shannon's logarithmic measure. Here we exhibit the existence of reciprocity relations between T-F and T and provide an interpretation with reference to the meaning of T-F for the canonical ensemble.