  A new statistical approach is presented to study the thermal instability
process of optically thin unmagnetized plasma. In this approach the time
evolution of mass distribution function over temperature is calculated. This
function characterizes the statistical properties of the multiphase medium of
arbitrary spaced three-dimensional structure of arbitrary temperature
perturbations. We construct our theory under the isobarical condition (P=const
over space), which is satisfied in the short wavelength limit. The developed
theory is illustrated in the case of thermal instability of a slowly expanding
interstellar cloud. Numerical solutions of equations of the statistical theory
are constucted and compared with hydrodynamical solutions. The results of both
approaches are identical in the short wavelength range when the isobarity
condition is satisfied. Also the limits of applicability of the statistical
theory are estimated. The possible evolution of initial spectrum of
perturbations is discussed. The proposed theory and numerical models can be
relevant to the formation of the two-phases medium in the ~1pc region around
quasars. Then small warm (T~10000K) clouds are formed as the result of thermal
instability in an expanded gas fragment, which is a product of either a
star-star or star-accretion disk collision.
