A new viewpoint of the mechanism of turbulent heat and mass transfer has been proposed; a mathematical apparatus of statistical theory and a method of construction of mathematical models under the conditions of intermittent dynamic and scalar fields of nonuniform turbulent flow have been developed. A model of a turbulent axisymmetric jet for evaluation testing of the method has been constructed and the conditional and total means of the basic statistical characteristics of the jet have been calculated. It has been shown that the reason for the “different mechanism” of turbulent transfer of momentum, heat, and substance is the intermittence of not coincident dynamic and scalar fields of turbulent flow. An equation for the conditional probability density function of the concentration of a passive impurity has been derived and its solution for the axisymmetric jet in a strongly intermittent region has been given. Good agreement between the performed calculations and experimental data confirms the adopted concept of the transfer mechanism.