An accurate theoretical analysis of the thermal creep slip velocityq˜T,asyfor arbitrary&agr;, the fraction of the molecules that are diffusely reflected from the surface, is carried out by applying the method of elementary solutions to the Bhatnagar‐Gross‐Krook model. Specifically,q˜T,asyis expressed in terms of two power series that, respectively, converge rapidly for&agr;→1and&agr;→0, and it is found thatq˜T,asydepends only slightly on&agr;. Some alternate forms of boundary conditions are also discussed, and it is shown that the thermal creep slip velocity does not depend on&agr;p, the momentum accommodation coefficient. These results confirm the essential accuracy of a very general variational expression given recently by one of the authors. Further, some consequences of the present results in the analysis of the thermal transpiration experiments are also discussed.