The behavior of a rarefied gas between two parallel plates with a sinusoidal temperature distribution is studied on the basis of the Boltzmann equation and the Cercignani-Lampis (CL) boundary condition. Numerical analysis by means of the direct simulation Monte Carlo (DSMC) method is carried out for a wide range of parameters with special interest in the free-molecular limit. The result shows that, contrary to the case of the Maxwell-type boundary condition, steady flows are induced by the effect of the temperature field even in the free-molecular gas. This fact is also confirmed by computations based on a deterministic method with higher accuracy.