  Correct phenomenological description of ferroelectric phase transitions in
barium titanate requires accounting for eighth-order terms in the free energy
expansion, in addition to the conventional sixth-order contributions. Another
unusual feature of BaTiO_3 crystal is that the coefficients B_1 and B_2 of the
terms P_x^4 and P_x^2*P_y^2 in the Landau expansion depend on the temperature.
It is shown that the temperature dependence of B_1 and B_2 may be caused by
thermal fluctuations of the polarization, provided the fourth-order
anharmonicity is anomalously small, i. e. the nonlinearity of P^4 type and
higher-order ones play comparable roles. Non-singular (non-critical)
fluctuation contributions to B_1 and B_2 are calculated in the first
approximation in sixth-order and eighth-order anharmonic constants. Both
contributions increase with the temperature, which is in agreement with
available experimental data. Moreover, the theory makes it possible to
estimate, without any additional assumptions, the ratio of fluctuation
(temperature dependent) contributions to coefficients B_1 and B_2. Theoretical
value of B_1/B_2 appears to be close to that given by experiments.
