In this paper we present a computational model to simulate momentum and heat transfer in complex micro-geometries. In particular, we present extensions to our previous work to incorporate a modified slip boundary condition we developed to include high-order Knudsen number effects as well as to take into account the coupling of momentum and heat transfer through thermal creep and viscous heating effects. Analytical results are derived for a pressure-driven channel flow and numerical tests are presented for a micro-channel and a slip-flow past a micro-cylinder.