A direct numerical simulation (DNS) of viscoelastic turbulent channel flow with a FENE-P model was carried out to investigate turbulent heat transfer mechanism of polymer drag-reduced flows. The configuration was a fully-developed turbulent channel flow with uniform heat flux imposed on both the walls. The temperature was considered as a passive scalar. Statistical quantities such as root-mean-square temperature fluctuations, turbulent heat fluxes and turbulent Prandtl number were obtained and compared with those of a Newtonian fluid flow. Budget terms of the temperature variance and turbulent heat fluxes were also presented.