An algebraic heat flux truncation model was derived for high-speed gaseous shear flows. The model was developed for high-temperature gases with caloric imperfections. Fluctuating dilatation moments were modelled via conservation of mass truncations. The present model provided significant improvements, up to 20%, in the temperature predictions over the gradient diffusion model for a Mach number ranging from 0.02 to 11.8. Analyses also showed that the near-wall dependence of the algebraic model agreed with expected scaling, where the constant Prandtl number model did not. This led to a simple modification of the turbulent Prandtl number model. Compressibility led to an explicit pressure gradient dependency with the present model. Analyses of a governing parameter indicated that these terms are negligibly small for low speeds. However, they may be important for high-speed flow.