The symmetry group of the non-isothermal Navier-Stokes equations is used to develop physics-preserving turbulence models for the subgrid stress tensor and the subgrid heat flux. The Reynolds analogy is not used. The theoretical properties of the models are investigated. In particular, their compatibility with the scaling laws of the flow are proven. A numerical test, in the configuration of an air flow in a ventilated and differentially heated room is presented.