This study concerns the near-wall behavior of the subgrid-scale diffusivity. This is shown to depend on the thermal boundary conditions. Therefore, the constant subgrid-scale Prandtl number hypothesis is questionable and a direct modeling of the subgrid-scale diffusivity is considered instead. Large-eddy simulations are carried out using the Trio U code in a turbulent channel flow configuration with the three classical thermal boundary conditions (constant temperature, constant heat flux, and adiabatic wall). Different dynamic methods are used to model the subgrid-scale diffusivity and results are compared with constant subgrid-scale Prandtl number large-eddy simulations and with direct numerical simulations.