Fluctuation effects on the order-disorder transition (ODT) in correlated random copolymers (polydisperse A/B multiblock copolymers with block lengths having an exponential Flory distribution, and a large average number of blocks per chain) are studied with due regard for the strong temperature dependence of the period of the arising ordered phases, characteristic for the system under consideration. To this end, following a field theoretical variational method, the free energy is minimized with respect to both the concentration profile psi and the correlation function G, assumed to belong to certain classes of trial functions. The trial function for G contains an extra adjustable parameter as compared to the situation typical for monodisperse A/B block copolymer melts. The shape of the correlation function and its temperature dependence are determined both for the disordered phase and for the ordered phases. In the vicinity of the critical point the phase diagram is calculated and presented in a universal form by using reduced variables. It is shown that near the ODT and for A-monomer fractions f close to 1/2, the profiles are strongly fluctuating : in the ordered phase the amplitude of the fluctuations is equal to the amplitude of the average profile, and in the disordered phase the concentration inhomogeneities are comparable to those in the ordered phase. In the same region the disordered phase has an anomalously large correlation length, indicating some kind of local ordering. In connection with this, we discuss the close relationship between the disordered phase and the random wave structure.