An anisotropic two-equation model is proposed to determine turbulent heat flux in a channel flow up to the wall. The turbulent heat fluxes are given in the form of an anisotropic eddy diffusivity representation in which both the isotropic and anisotropic eddy diffusivities of heat are expressed using the temperature variance $t2$, the dissipation rate of temperature fluctuations ϵt, and the velocity gradient. The proposed model is tested through application to an incompressible, two-dimensional, turbulent channel flow with the neglect of buoyant heat transfer. Calculated results are compared with the direct numerical simulation data. It is disclosed from the study that the proposed anisotropic $t2$-ϵt, heat transfer model predicts reasonably well the distributions of the time-averaged temperature, normal and streamwise turbulent heat fluxes, temperature variance, dissipation rates, and these near-wall budgets.