In this work we report on measurements, as a function of the temperature, of the nonlinear refractive indices parallel (n(2 parallel to)) and perpendicular (n(21)) to the nematic director near the reentrant isotropic-discotic nematic phase transition in a lyotropic mixture of potassium laurate, decanol and D(2)O. Thermal diffusivities, parallel (D(parallel to)) and perpendicular (D(perpendicular to)) to the director in this reentrant isotropic-discotic nematic phase transition, were also obtained as a function of the temperature from Z-scan experiment and interpreted through a thermal lens model. The ratios n(2 parallel to)/n(2 perpendicular to) and D parallel to/D(perpendicular to) are less than one in this nematic phase. These results are discussed in terms of structural changes in the micellar configuration which takes place in each nematic phase transition.