Based on the second-order model suggested by Kolovandin and Martynenko (Heat/mass transfer in homogeneous turbulence, 9th Int. Heat Transfer Conf., Jerusalem (1990)) numerical modelling of the nearly homogeneous turbulence of the velocity and transported passive scalar fields is considered. The work is aimed at a detailed study of the effect exerted by the basic factors of turbulence generation—the gradients of the averaged velocity and scalar values—on the evolution in time of the statistical characteristics of turbulence which, within the framework of the second-order model, determine the processes of turbulent momentum and heat transfer at arbitrary turbulent Reynolds and Peclet numbers.