The results of experimental and theoretical studies of the unsteady mixing process of heat carrier in a helical tube bundle when heat carrier flowrate is increased and decreased are presented. In experiments, the axisymmetric nonuniformity of a heat release field was modeled and temperature fields of heat carrier were measured at the tube bundle cross-section. Theoretically, the temperature fields were calculated using the two-temperature flow model of a two-phase homogenized medium with a stationary solid phase. Effective turbulent transfer coefficients were determined from comparison of the experimental and predicted temperature fields of heat carrier. New generalizing relations are derived to calculate effective turbulent transfer coefficients used to close a system of equations describing unsteady thermal and hydraulic processes in such tube bundles. The physical phenomena that characterize the specific features of heat transfer from flow swirling in complex-geometry channels for different types of hydrodynamic unsteadiness are considered. Examples of calculation of transient processes, as applied to a vehicular nuclear reactor, are presented.