This paper extends the hybrid computational method proposed by Docherty et al. (2014) for simulating non-isothermal rarefied gas flows at the microscale. Coupling a continuum fluid description to a direct simulation Monte Carlo (DSMC) solver, the original methodology considered the transfer of heat only, with validation performed on 1D micro Fourier flow. Here, the coupling strategy is extended to consider the transport of mass, momentum, and heat, and validation in 1D is performed on the high-speed micro Couette flow problem. Sufficient micro resolution in the hybrid method enables good agreement with an equivalent pure DSMC simulation, but the method offers no computational speed-up for this 1D problem. However, considerable speed-up is achieved for a 2D problem: gas flowing through a microscale crack is modelled as a microchannel with a high-aspect-ratio cross-section. With a temperature difference imposed between the walls of the cross-section, the hybrid method predicts the velocity and temperature variation over the cross-section very accurately; an accurate mass flow rate prediction is also obtained. (C) 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.orgilicensesiby/4.0/).