This paper analyzes the results of accurate measurements of the ion current collected by a cylindrical Langmuir probe immersed in cold argon, neon, and helium plasmas. These measurements make it possible to study the influence of the positive ion-to-electron temperature ratio β = T + /T e on the collected ion current, providing valuable information about the trajectory described by the positive ions when falling toward the probe. Several criteria have been applied to discriminate whether the ion current is described by using the orbital motion limited theory or the radial motion theory. In all the studied argon and neon plasma discharge conditions, the criteria indicate that the positive ion current collected by the probe is appropriately described by the radial motion theory; however, as β increases, some criteria indicate a trend toward the orbital theory. In contrast, for the studied helium plasmas discharge conditions, a transition from radial to orbital motion has been measured.