The dilute regime of the lamellar phase in the SDS/pentanol/water/dodecane system is investigated by H-2 and Na-23 NMR. From the reduction of the quadrupole splitting on dilution, we determine-the temperature and composition variation in the bilayer bending rigidity kappa. We find an essentially temperature independent kappa = (9 +/- 1) x 10(-21) J in the range 0-60 degrees C. The variation in kappa with the bilayer composition displays an increasing rigidity on removing pentanol and water from,the bilayer. The composition and temperature variation in kappa correlate with the extension of the lamellar phase in the phase diagram The predictions of recent theories for the molecular interactions contributing to kappa-mainly the hydrocarbon tail conformational entropy and the electrostatic interactions in the polar region-can account for the experimental results.