We generalize the phenomenological Landau-de Gennes theory of biaxial nematics by including fluctuations of the tensor order parameter. Then, using real-space Monte Carlo simulations we study how these fluctuations affect relative stability of the isotropic phase, the uniaxial nematic phase and the biaxial nematic phase of D(2h) symmetry. Results are confronted with earlier predictions of Landaude Gennes theory.