According to the thermodynamical analogy in black hole physics, the entropy of a black hole in the Einstein theory of gravity iswhere A H is the area of a black hole surface and l P = (hG/c 3 ) 1/2 is the Planck length [1,2]. In black hole physics the Bekenstein-Hawking entropy S BH plays essentially the same role as in the usual thermodynamics. In particular it allows to estimate what part of the internal energy of a black hole can be transformed into work. Four laws of black hole physics that form the basis in the thermodynamical analogy were formulated in [3]. According to this analogy the entropy S is defined by the response of the free energy F of the system containing a black hole to the change of its temperature:The generalized second law [1, 2, 4] (see also [5,6,7,8] and references therein) implies that when a black hole is a part of the thermodynamical system the total entropy (i.e. the sum of the entropy of a black hole and the entropy of the surrounding matter) does not decrease. The Euclidean approach [9, 10, 11] provides a natural way to derive black hole thermodynamical properties. Doing a Wick's rotation t → −iτ in the Schwarzschild metric one gets the metric with the Euclidean signature. The corresponding manifold with the Euclidean metric is regular if and only if the imagine time τ is periodic and the period is 2π/κ, where κ is the surface gravity of the black hole. The corresponding *