We calculate the energy eigenvalues of the channeled positrons through single wall carbon nanotubes (n,m). According to the continuum model approximation given by Lindhard for the case of an axial channeling in single crystals, the actual periodic potential of a row of atoms is replaced by a potential averaged over a direction parallel to the row, called continuum potential. The calculations was executed by using the atomic interaction potential as given by Moliere potential and Biersack's universal potential. The maximum number of bound states and the energy eigenvalues is calculated for positrons of 100 MeV energy incident in a direction parallel to the nanotube axis, by using WKB method. The calculations showed that the estimation of the maximum number of bound states of the channeled positron in armchair, chiral, and zigzag nanotubes is higher for the Moliere potential than for the Universal potential. The calculations showed that the effect of temperature by using Debye approximation of thermal vibration amplitude on the channeling potential is very small and gave the same eigenvalues and the same number of bound states as that for the static nanotubes.