This article present the theoretical analysis of gas flow and heat transfer in micro rectangular channels in the regime of velocity slip and temperature jump. The model is built on the assumption that the bottom wall of the channel is in uniform heat flux while the other three walls are adiabatic, and that the flow and heat transfer is of the hydraulic and thermal fully developed laminar flow of the incompressible fluid. Analytic solutions of the cross section distributions of both the velocity and temperature are obtained.The friction and heat transfer performances are discussed. The agreement between analytic solutions and experimental results existed shows that in a definite extension of Knudsen number the traditional Navier Stoks equations and energy equations with the boundary conditions of slip velocity and temperature jump can describe the gaseous flow and heat transfer mechanisms in micro rectangular channels.