The testing of the standard and modified SST models of the transfer of shear stresses was carried out on an example of calculating the heat transfer with an intense detached flow around a conical dimple with a slope angle of 45° on the heated wall of a narrow channel. It was shown that the standard turbulence model by Menter SST (MSST) of 2003, widely used in the packages Fluent, CFX, StarCCM+, etc., significantly underestimated the intensity of the return flow. A correction of this model was presented that took into account the influence of the curvature of streamlines within the framework of the Rodi-Leshziner-Isaev (RLI) approach for spatial separated flows. It was found that the predictions for the RLI MSST 2003 were close to the predictions for the original standard MSST 1993, in which the eddy viscosity was calculated using the vorticity modulus. At the same time, the predictions based on the modified one, following Smirnov-Menter (SM) MSST 2003, included in the ANSYS model catalog did not differ too much from the standard MSST 2003. The preference of the MSST modified within the RLI 2003 for calculating the heat transfer in intense separated flows was substantiated.