An investigation has been made of the validity of the perfectly conducting sphere model used in the calculation of drag forces acting on spheres moving in rarefied gases. This assumption requires that the frictional heat generated by the motion of the sphere is conducted so rapidly through the material that the surface temperature is everywhere constant. In turn this affects the energy of the atoms reflected from the surface of the body and hence the drag experienced by it. Instead, there-fore, of making this a priori assumption, we allow the sphere to have an arbitrary thermal con-ductivity. We then solve the heat conduction equation in the sphere and relate it to the external gas conditions by computing the heat transfer rate caused by gas atom collisions. The theory so developed is applicable for arbitrary speed but, for simplecity in this introductory paper, we obtain some analytical results for speeds very much less than Mach one. Our conclusions indicate that the effects of finite conduction on the drag forces are generally small, even when the sphere is a thin shell with a non-conducting interior. Indeed, it is not difficult to show that in going from a perfect thermal conductor to a perfect thermal insulator the drag force only increases by about 3%; nevertheless, in some situations this may well be important and inter-mediate cases will have to include the correction term. More significantly, however, the surface temperature on the sphere is shown to depend on the conductivity to a much greater degree, with the leading face being appreciably hotter than the trailing one. The general conclusion is that for most practical problems involving small particles in the Knudsen regime, moving at appreciably sub-sonic speeds, the assumption of the perfect thermal conductor is a good one.