This paper presents a novel methodology for improving eddy viscosity models in predicting wall-bounded turbulent flows with strong gradients in the thermo-physical properties. Common turbulence models for solving the Reynolds-averaged Navier–Stokes equations do not correctly account for variations in transport properties, such as density and viscosity, which can cause substantial inaccuracies in predicting important quantities of interest, for example, heat transfer and drag. Based on the semi-locally scaled turbulent kinetic energy equation, introduced in [Pecnik and Patel, J. Fluid Mech. (2017), vol. 823, R1], we analytically derive a modification of the diffusion term of turbulent scalar equations. The modification has been applied to five common eddy viscosity turbulence models and tested for fully developed turbulent channels with isothermal walls that are volumetrically heated, either by a uniform heat source or viscous heating in supersonic flow conditions. The agreement with results obtained by direct numerical simulation shows that the modification significantly improves results of eddy viscosity models for fluids with variable transport properties.