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Opto-acoustical gravitational detector OGRAN composed by the aluminum bar with optical FP cavity along its longitudinal axis is in assembling into a deep underground of the Baksan Neutrino Observatory. Under room temperature the sensitivity of this setup does not exceed 10^-19 in term of metrics perturbation [1]. This limit is defined by the bar Brownian noise. The only possibility of the sensitivity increasing is associated with the bar cooling. The deep cooling up to helium temperature (and below) requires a very complex and expensive cryostat, similar to the cryogenic bar detector setups like Explorer and Nautilus [2]. The numerical analysis performed in our group has shown that for the opto-acoustical detector the moderate cooling at the nitrogen temperature level allows to achieve the sensitivity increased on two orders of value up to 10^-21 . However the problem of FP cavity with cooled mirrors in the presence of high power optical pump has to be specially investigated . [3]. We present some experimental data collected at the cooled bar model with mirrors on substrates type of CaF2 and SITAL concerning the FP cavity finesse evolution under variations of the temperature and pump power. [1] Bagaev S.N., Bezrukov L.B., Kvashnin N.L.,Krysanov V.A., Oreshkin S.I., Motylev A.M, Popov S.M., Rudenko V.N., Samoilenko A.A., Skvortsov M.N., and Yudin, I.S. A high frequency resonance gravity gradiometer. Review of Scientific Instrument 85, 065114 (2014). [2] P. Astone, D. Babusci, L. Baggio et al., Phys. Rev. D 76, 102001 (2007). [3] M. Punturo, M. Abernathy, F. Acernese et al., Classical Quantum Grav. 27, 084007 (2010).