This study examined the heat transfer reduction in drag-reduced turbulent flows of dilute polymer solutions. To this end, direct numerical simulations of fully developed viscoelastic turbulent channel flows (Reτ = 125 and Pr = 5) were conducted under a constant heat flux boundary condition. The polymer stress was modeled using the finitely extensible nonlinear elastic-Peterlin constitutive model, and low (15%), intermediate (34%), and high drag reduction (52%) cases were examined. In drag-reduced flows, the turbulent transport of momentum and heat were still analogous, similar to the case of Newtonian flow; however, the Colburn analogy cannot be applied. Further, the two-point correlations between the temperature fluctuations and velocity components were almost identical to those of the streamwise velocity fluctuations. In addition, the spectral density distribution of the turbulent heat flux was found to be similar to that of the Reynolds shear stress in both Newtonian and drag-reduced flows. The conditionally averaged fields for the events that considerably contributed to the wall-normal turbulent heat flux were quite similar to those for the second quadrant events most contributing the Reynolds shear stress in both Newtonian and viscoelastic flows. The results of the study indicated that the turbulent transport of momentum and heat are associated with approximately identical flow structures in drag-reduced and Newtonian flows. Furthermore, an analysis of the three-dimensional joint probability density function clearly confirmed that the turbulent motions contributing to the Reynolds shear stress contributed equivalently to the turbulent heat flux in both Newtonian and drag-reduced flows.