An analysis of experimental heat-transfer results taken over fairly broad ranges of the pertinent variables is presented for purposes of establishing the major heat-transfer characteristics of these systems and delineating the areas in which further and more detailed studies may be helpful These results, when analyzed in terms of the analogy equations, suggest major decreases to occur in the eddy transport coefficients, at least in wall regions, when the fluid elasticity level, as measured by its relaxation time, is increased to the level of 10 −3−10 −2 s. This tentative conclusion is of importance from the viewpoint of defining in part the structure of the turbulence in these systems, as direct measurements with the usual kinds of turbulence probes may be difficult or even impossible to carry out. Thus the present results also suggest that the very low drag coefficients frequently observed with these systems do not arise as a result of a “conservative”, as opposed to a “dissipative”, turbulent field but rather because of the strong suppression of turbulence in the fluid when the Deborah number of the flow becomes sufficiently great.