Drag-reducing solutions exhibit simultaneous friction and heat transfer reductions, yet it has been widely believed that there is no direct coupling between the two. In this work, we have conducted a study to re-examine this issue, using measurements of friction and heat transfer over a wide range of flow conditions from onset to asymptotic, various pipe diameters, and several polymer and surfactant solutions. Contrary to some earlier suggestions, our tests show that no decoupling of the momentum and heat transfer mechanisms was seen at the onset of drag reduction, nor upon departure from the asymptotes, but rather that the friction and heat transfer reductions change simultaneously in those regions. For asymptotic surfactant and polymer solutions, the ratio of heat transfer and drag reductions was seen to be constant over a large range of Reynolds numbers, if modified definitions of the reduction parameters are used. In the nonasymptotic region, however, the ratio of heat transfer to drag reductions is higher and is a function of the reduction level, but is approximately the same for polymer and surfactant solutions. This variation is consistent with the concept of a direct coupling through a nonunity constant Prt, as also suggested by our local measurements of temperature and velocity profiles. We also saw that our diameter scaling technique for friction applies equally well to heat transfer. These findings allow us to predict directly the heat transfer from friction measurements or vice versa for these drag-reducing fluids, and also suggest that a strong coupling exists between the heat and momentum transfer mechanisms.