The transition hexagonal phase/fluid isotropic phase in the nonionic binary system C12EO6/water is studied. The birefringence of a planar monodomain and the water deuterium NMR splitting are measured as functions of the temperature in the hexagonal phase, at the azeotropic concentration. The planar monodomain is obtained by directional solidification. It is shown that important pretransitional effects exist on approaching the transition. These effects are interpreted as due to the appearance of defects which announce the high-temperature isotropic phase. These defects may consist either of a fragmentation of the columns in segments of finite length or of bridges connecting neighboring cylinders. The activation energy associated with these defects is estimated to be of the order of 0.13 eV/surfactant molecule. The mean length between defects along a column at the transition is estimated to be of the order of 80 nm. Finally an estimate is given for the curvature and saddle splay elastic constants of the monolayer.