Pluronic L64 triblock copolymer is soluble in water at room temperature up to more than 30 wt%, forming disordered spherical micellar phase above the cmc-cmt line. We investigate the structure and interaction between these micelles at temperature approaching the cloud point curve at approximate 57 degrees C along isoconcentration lines. An extensive light scattering intensity measurement indicates that the critical concentration is about 5wt%. We use a previously developed cap-and-gown model for calculating the micellar structure factor and a sticky hard sphere model for the intermicellar structure factor. SANS intensity distribution is fitted with four parameters: the aggregation number of micelle N, the hydrophobic core radius a, the overall hard sphere volume fraction phi, and the stickiness between micelles 1/tau. The model is found to describe all SANS data satisfactorily in absolute scale. As one approaches the cloud point curve at constant weight fraction, the aggregation number increases, the micellar core becomes dryer, and the stickiness parameter increases. In particular, at weight fraction of 5%, the stickiness parameter approaches the critical value 10.2 at T=330.9 K. We thus conclude that there is a critical demixing point in this micellar solution where micelles interact strongly with each other by a short range temperature dependent attraction.