A model for the turbulence dissipation rate in stably stratified shear turbulence is developed and validated. The functional dependence of the model is derived from first principles and it represents a conceptually new approach in that it depends on the background temperature field rather than on the fluctuating velocity field. This novel feature makes the proposed model a viable candidate for dissipation rate estimates in measured real-life flows. Direct numerical simulation data are used for a priori assessment of the proposed model. It is demonstrated that the proposed model performs very well, particularly in cases where the background stratification becomes dynamically important. Also, a generalized expression for the mixing coefficient has been rigorously derived from first principles assuming local isotropy of incompressible turbulent flows. The mixing coefficient is shown to depend on the Prandtl number and values are in correspondence with previous studies.