Interest is significant in the ability to numerically predict the gas flows in microchannels. One of the reference methods used for this purpose is the DSMC method by Bird (Aktas et al., J Microelectromech S 10:538–549 (2001) [1]; Bird, Gas dynamics and the direct simulation of gas flows. Clarendon Press (1994) [2]). Although effective, this statistical method requires significant computational resources. A more economical alternative is to use an asymptotic model. We use this approach in the case of a planar microchannel whose thickness varies sinusoidally and whose wall temperature is a function of the longitudinal spatial variable. We are interested in the case of flows of a mixture of two inert gases with a low Mach number and a Knudsen number of the order of \(10^{-1}\) . These flows correspond to the slip flow regime. As a consequence, the Navier-Stokes-Fourier equations remain valid, provided they are supplemented with slip conditions for velocity and temperature. The aim of this contribution is to study the effects of the channel cross-section function on the flow parameters.