With the help of a theory which is based on functional integrals, we calculate the evolution, with temperature and degree of polymerization, of the orientational order parameter of thermotropic nematic polymers under a magnetic field. We compare our results with those obtained experimentally from magnetic birefringence measurements on polyesters. The validity of the application of the mean-field theory in the case of semiflexible liquid crystal polymers which consist of sequences of mesogenic units and flexible spacers is also discussed.