We demonstrate here, for the first time, the constitutive scaling approach applied to simulate a fully compressible, non-isothermal gas microflows within a mainstream computational physics framework. First, the physics underlying constitutive-relation scaling models is discussed, including the effects of velocity slip, temperature jump and the Knudsen layer. Results for Couette-type flows in micro-channels, including heat transfer effects, are then reported and we show comparisons with both traditional Navier-Stokes-Fourier solutions and independent numerical studies. We discuss the limitations of the constitutive scaling process, such as the breakdown of the model as the Knudsen number increases and the influence of the wall interaction model on the numerical results. Advantages of the constitutive scaling technique are described, with particular reference to the practicality of using it for microscale engineering design. (C) 2007 Elsevier Ltd. All rights reserved.