We report on the third phase of our study of the neutrino-cooled hyperaccreting torus around a black hole that powers the jet in Gamma Ray Bursts. We focus on the influence of the black hole spin on the properties of the torus. The structure of a stationary torus around the Kerr black hole is solved numerically. We take into account the detailed treatment of the microphysics in the nuclear equation of state that includes the neutrino trapping effect. We find, that in the case of rapidly rotating black holes, the thermal instability discussed in our previous work is enhanced and develops for much lower accretion rates. We also find the important role of the energy transfer from the rotating black hole to the torus, via the magnetic coupling.
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